University of Sudan for Sciences and Technology
College of Graduate Studies
A thesis submitted for the degree of M.Sc. in Statistics
بحث مقدم لنيل درجة الماجستير في اإلحصاء
In title:
بعنوان: Use of Plot Size in Estimation of Crops Yield per feddan In Traditional Rain-fed Sector (Sorghum) at period 2015/2016 إستخدام حجم الحوض في تقدير إنتاجية الفدان للمحاصيل في القطاع التقليدي )الذرة( خالل الفترة 2016/2015
By: Supervisor:
Hamza Abdalla Siror Dr. Amal Alsir Alkhidir
September 2016
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اآلية
بسم هللا الرحمن الرحيم
قال تعالى: أفرأ يتم ما تحرثون )63( أأنتم تزرعونه أم نحن الزارعون )64(
سورة الواقعة أآليات )63 – 64(:
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DEDICATION
This thesis is dedicated to soul of my parents who were emphasized the importance of education and worked very hard and exert efforts to educate me and my brothers and sisters throughout their life. The dedication extends to my wife and children.
I dedicate this Master’s dissertation to all who have been and still fighting to promote and improve their knowledge and skills of statistics.
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ACKNOWLEDGEMENTS
First of all, I express my gratitude to Dr. Amal Alsir Alkhidir for granting me the opportunity to complete this work under her guidance. Thank you for coaching inputs and feedback.
Next, I could never thank enough to my family for their constant and unconditional support, understanding and faith. I know you will always be there for me.
Special thanks to Mr. Hassan Elsheikh for his friendliness, kindness, open mindset and energetic attitude, I have learned many things from him.
To my friends Azhari, Bushra, Gamal, Amna and Elham – thank you for your support, help and encouragement in pursuing my dreams!
Finally, I want to thank the Sudan University of Science and Technology for organizing this programme, especially all administrative and academic staff of college of science, department of statistics that were responsible for realization of the statistic programme. Your efforts in day- to-day activities, excellence and passion for science have been highly appreciated and truly inspiring.
However, apart from all the valuable academic knowledge and practical skill I have gained during my studies, I feel that the most valuable thing I am taking with me is to dare to think.
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ABSTRACT
The rain-fed traditional represent a big share of area cultivated in the Sudan and characterized by a very complicated situation leads to numbers of problems in agricultural statistics, in respect to area enumeration and yield estimation and poses serious threats to quality and reliability of area and production estimates. Due to these problems it is essential to pay more attention to this important sector.
The study was carried out to study the effect of plot sizes on the three different types of soils (sandy, loam and clay soils) on the estimation of sorghum yield in the traditional rain-fed sector. The estimation was obtained by using crop-cutting technique and multi-stage stratified sampling. The primary data obtained from different plot sizes namely 5x5m, 6x7m and 10x10m on each type of soil. Equal sample size allocation was used. The village was considered as primary sampling unit and the field as secondary sampling unit and the plot as third sampling unit. Sample size of twenty for each plot size and on each soil type was used, with the following hypothesis;
1-There is a direct relationship between plant density and plot size.
2-The margin of error reflects the required sample size and there is a direct correlation between the level of accuracy required and the cost of conducting survey.
3-Increase of plot size has no effect on either the precision or the accuracy.
Analysis of variance table was used to analyze the effect of sample sizes on the estimation of sorghum yield in traditional rain-fed sector. The coefficient of variation was used to identify the best stable crop yield according to the plot size. The multiple comparison method was used to detect the significant differences between means in each soil type according to the plot size by using statistical package SPSS.
The results shows and according to the conclusions of the study the plot size had not shown any effect on the yield in the different types of soils, but there was slight effect of plots size in case of plants density estimation. There seem other factors affecting the level of yields. These
iii factors should be planting spaces, seed rate, adequate re-sowing, thinning and optimum sowing dates.
Two recommendations were recommended:
1- If the main objective of the survey is to estimate the crop yield, then the small size plots are better and recommended to use in all types of soils to save time and to save resources. 2- If the objective of the survey is to estimate the plant density then the medium plots size are better in estimation and recommended to be used.
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المستخلص
يمثل القطاع التقليدىالجزء االكبر من المساحة المزروعة في السودان ويتصف بوضعه المعقد مما نجمت عنهمشاكل كبيرة فى االحصاءات الزراعية, تتمثل فىتحديد المساحات المزروعة واالنتاجية الشئ الذى اثر كثيرا علي جودة ومصداقية المعلومة مما يجعل من االهمية بمكان االلتفات الي هذا القطاع الهام.
هدفت الدراسة الي دراسة اثر حجم االحواض في ثالثة انواع من الترب الزراعية علي تقدير انتاجية الذرة فى القطاع المطري التقليدى. توصلنا الي التقدير باستخدام طريقة قطع المحصول واستخدام العينة الطبقية متعددة المراحل.
البيانات االولية حصلنا عليها باستخدام ثالثة احواض مختلفة المساحة وهي تحديدا 5*5 متر, 6*7 متر و10*10 متر في كل نوع من انواع الترب الزراعية الثالث. اعتبرت القرية كوحدة احصائية اولية والمزرعة كوحدة احصائة ثانية واالحواض كوحدة احصائية ثالثة.
عشرون عينة لكل حجم حوض فى كل نوع من انواع الترب الزراعية وهي التربة الرملية والتربة الطينية الخفيفة والتربة الطينية الثقيلة قد تم استخدامها. وكانت فرضيات البحث كاالتى:
1- هنالك عالقة مباشرة بين الكثافة النباتية وحجم الحوض. 2- هامش الخطا يعكس حجم العينة المطلوب وهنالك عالقة بين مستوى الدقة المطلوب وتكلفةتنفيذ المسح. 3- حجم الحوض لبس له اثر علي الدقة والجودة تم استخدام جدول تحليل التباين لتحليل اثر حجم الحوض علي تقدير االنتاجية فى القطاع التقليدى. معامل االختالف تم استخدامه لمعرفة االستقرار فى تقدير االنتاجية حسب مساحة الحوض. ايضا تم استخدام طريقة المقارنات المتعددة لتحديد الفروقات المعنوية بين المتوسطات فى كل نوع من انواع الترب الزراعية حسب حجم الحوض وذلك باستخدام البرنامج االحصائى SPSS.
اظهرت نتائج الدراسة انه ال اثر لحجم الحوضعلي تقدير االنتاجية في الترب الثالث. لكن هنالك اثر طفيف لحجم الحوض في حالة تقدير الكثافة النباتية. وقد يعود ذلك البعاد الزراعة وكميات التقاوى للفدان, الرقاعة, الشلخ وتاريخ الزراعة المناسب.
خرج البحث بتوصيتين:
1- لتقدير االنتاجية حجم الحوض الصغير هو االفضل وعلى جميع انواع الترب الزراعية لتوفير الزمن والموارد. 2- لتقدير الكثافة النباتية االفضل استخدام حجم الحوض المتوسط.
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Table of contents
Item Page Aya of The Quran ⁱ Dedication ⁱⁱ Acknowledgements ⁱⁱⁱ Abstract іv Table of contents vіі List of tables іx CHAPTER ONE - Introduction 1 1-1 Preface 2 2-1 Research Problem 2 3-1 Research Importance 3 4-1 Objective of the Research 3 5-1 Hypothesis of the Research 3 6-1 The Research, Methodology 4 7-1The Research Area of the Study 4 8-1 Previous Studies 4 9-1 Research Structure 5 CHAPTER TWO - Rain-Fed Traditional Sector 6 1-2 Preface 7 2-2 Traditional Rain-Fed Agriculture 7 3-2 Traditional Sector 10 4-2 Contribution of the Sector to the Export Value 10 5-2 Traditional Rain-fed Agriculture Subsistence Oriented 11 6-2 Performance of the Traditional Rain-fed Sector 11 7-2 Historical Background of Agricultural Statistics in Sudan 12 8-2 Method of Collection Agricultural Data in the Irrigated Sector 14 9-2 Rain-fed Mechanized Sector 15 CHAPTER THREE – Literature review 17 1-3 The notion of survey sampling 18 2-3 Survey sampling 18 3-3 Observational access to the population 21 4-3 Important and desirable properties of a frame 24 5-3 Simple random sampling 26 6-3 Stratified sampling 28 7-3 Cluster Sampling 34 8-3 Systematic Sampling 37 9-3 Estimating the Variance 38 10-3 Non-sampling Error 38 11-3 Agricultural Surveys 39 12-3 Measurement of Estimator Quality 39 13-3 Standard Deviations 40 14-3 Standard Errors 40 15-3 Coefficient of Variation 40 16-3 The Estimation of the Production 40
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17-3 Some Sampling Surveys in Sudan 43 18-3 Rain-fed Mechanized Sector 45 19-3 Some Surveys in Egypt and India 45 20-3 Research Type 46 21-3 Assessment Methodology 48 22-3 Multiple Comparison of the Means Procedure 51 CHAPTER FOUR 54 1-4 The Analysis and Results Discussion 55 CHAPTER FIVE 63 1-5 Conclusion 64 2-5 Recommendation 65 References 66 Annexes
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List of Tables
No. ITEM Page Table 1-2 Area harvested Production & Average Yield of Sorghum and Sesame 6 (90/91 – 2014/2015) Table 1-3 Two Stage Estimation 45 Table 2-3 Two Stage Estimation Analysis of Variance 46 Table 3-3 The Estimation of the Overall Yield 47 Table 4-3 Three Stage Estimation Analysis of Variance 48 Table 1-4 Mean statistics for number of heads per feddan under different plot 51 sizes (Fershaya Area) Table 2-4 Analysis of Variance (Fershaya Area) 51 Table 3-4 Sub-set Homogeneous (Fershaya Area) 52 Table 4-4 Mean statistics for number of heads per feddan under different plot 52 sizes (Debaibat Area) Table 5-4 Analysis of Variance (Debaibat Area) 52 Table 6-4 Sub-set Homogeneous (Debaibat Area)) 53 Table 7-4 Mean statistics for number of heads per feddan under different plot 53 sizes (Dalami Area) Table 8-4 Analysis of Variance (Dalami Area) 53 Table 9-4 Sub-set Homogeneous (Dalami Area) 54 Table 10-4 Mean statistics for average yield per feddan under different plot sizes 54 (Fershaya Area) Table 11-4 Analysis of Variance (Fershaya Area) 54 Table 12-4 Sub-set Homogeneous (Fershaya Area) 55 Table 13-4 Mean statistics for average yield per feddan under different plot sizes 55 (Debaibat Area) Table14-4 Analysis of Variance (Debaibat Area) 56 Table 15-4 Sub-set Homogeneous (Debaibat Area)) 56 Table 16-4 Mean statistics for average yield per feddan under different plot sizes 56 (Dalami Area) Table 17-4 Analysis of Variance (Dalami Area) 57 Table 18-4 Sub-set Homogeneous (Dalami Area) 57
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CHAPTER ONE Introduction
1-1 Preface 2-1 Research Problem 3-1 Research Importance 4-1 Objective of the Research 5-1 Hypothesis of the Research 6-1 The Research Methodology 7-1The Research Area of the Study 8-1 Previous Studies 9-1 Research Structure
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Chapter One Introduction 1-1 Preface: Sudan is basically an agriculture-dominated country, where cultivation is usually carried out in three main sectors, namely irrigated sector, mechanized rain-fed sector and traditional rain-fed sector. The agriculture activities are governed by agro climatic conditions having divergent features spread over the length and broads of the country. Number of food and nonfood crops is sown in different areas of the country depending on climatic conditions and other environmental factors. 2-1 Research problem: The traditional rain-fed sector cultivation is carried out as a household enterprise and because of its large contribution in the national economy and of the different crops sown in this sector a reliable statistics becomes of a very importance .One of the most important factors for the production used in growing crops, raising livestock or any other farming activity is land. In traditional sector the pattern of land use usually varies by seasons or by different regions of the country. Thus apart from being used in the estimation of agricultural production, accurate data on area used for agricultural purposes is important aspect of agricultural planning. The total land operated by the holder [i.e. the agricultural holding] is a crucial variable for the analysis of agricultural data. The area of a holding may vary from time to time; a holder may sell or leave part of his holding or may buy or rent from others. Thus the proportion of the holding under crop also varies from season to season or from year to year. This very complicated situation in traditional sector leads to numbers of problems in agricultural statistics, in respect to area enumeration and poses serious threats to quality and reliability of area estimates There are three types of errors that may occur if we depend on fieldworker's reports of area cultivated to be used as a frame for sample selection. These errors are: 1- Non-reporting of crops actually grown in the field 2- Reporting of crops not grown. 3- Incorrect reporting of area under crops
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3-1 Research Importance: Agriculture plays a dominant role in the Sudan economyas more than 70% of the populations are engaged directly or indirectly in this activity. Despite its diminishing contributions in the overall exports earnings, after the discovery and export of oil in the late 90s yet agriculture share in GDP still represents about 45%. Such an essential activity needs an efficient information system that provides decision makers, planers, researchers and data users with appropriate, accurate and timely data. The agricultural information system must fulfill the following:- 1- Identify the information required for the most important and public decisions and specify the kinds of information that deserve highest priority. 2- Utilize methods and means of collecting, processing, analyzing, and presenting data that meet reasonable standards of accuracy, coverage and timeliness, while at the same time try to minimize financial and human costs. 3- Have institutional structure which brings users and suppliers of information in a continuous dialogue and which is able to adapt itself to the changing demands of information and modern methodologies for generating it. Despite the general perception and understanding of the importance of information system by decision maker, politicians, planners, and most categories of data users, but still there is a wide gap between the understanding and adoption and application reality, and in fact the standard of agricultural statistics is even deteriorating in recent years. 4-1 Objectives of the research: 1/is to estimate the average yield per feddan and consequently estimate the total production of sorghum. 2/ is to estimate harvested area depending on response from the selected farmers identifying planted and harvested areas. 3/ the same sample or a sub sample can be used to collect information on cost of the production and marketing of agricultural products. 5-1 Hypothesis of the Study: 1- Relationship between population size and sample size is not directly proportional 2- The margin of error impacts the required sample size and there is a direct correlation between the level of accuracy required and the cost of conducting survey. 3- Increase of plot size has no effect on either the precision or the accuracy.
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6-1 The ResearchMethodology: Attempt which aim at finding and recommending the most accurate and practicable method to be use in traditional sector to: 1- Introducing measures for improvement in the system of data collection relate to timely reporting to reduce the time lag between the completion of sowing and the availability of the estimates of area sown in respect to importance of crops 2- Estimate the area cultivated under different crops to be used as a frame for productive area and yield estimation compare different sizes of plots used in crop-cutting surveys for the estimation of average yield per feddan and recommending the best and most accurate one The research sampling design for check on area enumeration and crop yield estimation to be use for comparison of different plot sizes are by using crop-cutting as follows: Stratified three stages random sampling of equal allocation, with three identified strata in the locality [namely loam soil, sandy soil and clay soil] as main domain of research, villages within the stratum as first stage units and survey numbers [household] within villages as second stage units and plots within the farms as the ultimate sampling units, following simple random sampling without replacement. The analysis is carried out using SPSS packages for the manipulation and statistical analysis of data to get descriptive statistics and inferences of research results. 7-1 The research area of the study: The study should be carried out in Dilling locality in South Kordofan state. The locality found in the middle of the north part of South Kordofan state. It was characterized by its diversity in soil and crops and considered as traditional cultivation dominated locality, although there are large areas under mechanized rain-fed sector 8-1previous studies: The previous studies carried out in the Sudan using crop cutting methodology are mainly on the mechanized rain-fed sector and to some extend on the irrigated sector. The design was stratified two stage random sample with uniform sampling fraction (proportionate allocation). The producing centres of the mechanized rain-fed sectors were considered as a domain area of the study and a sampling error of 5% of the average yield was contemplated. For the specified degree of accuracy, it was decided that and after many years of surveys,500 sample size to be
4 conducted in Gedaref, 300sample in Blue Nile, and same in Sennar and White Nile. Blocks were considered as the main strata and section within blocks as sub strata. All the first stage of sampling and number of farms (selection) is selected randomly from each section within each block. This number is proportionate to the size area sown in that section. In this second stage of selection, two plots are randomly selected within each selected farm, the size of plot being 5*5 meters = 1/168 feddans but in the irrigated the plot size being 3x3 meters = 1/667 feddans. The selected plots were harvested, the number of heads recorded, weighted set and dry, threshed and the grain weighted simple weighted averages together variance and sample errors were computed to calculate the average yield per feddan and confidence limits forthe total production expected for each section and block, and accordingly the weighted average together with the maximum and minimum yield expected at the level of the producing center. 9-1 Research Structure: This study includes five chapters, Chapter one consists the introduction, research problem, objective of the study, area of the study, research hypotheses, & research methodology. Chapter two provides an overview of rain-fed traditional sector and historical background of agricultural statistics in the Sudan. Chapter three presents literature review of survey sampling and methods of assessment.Chapter four provides research analysisand results discussion. Chapter five focuses on the findings, conclusion & recommendation of the research.
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CHAPTER TWO - Rain-Fed Traditional Sector 1-2 Preface 2-2 Traditional Rain-Fed Agriculture 3-2 Traditional Sector 4-2 Contribution of the Sector to the Export Value 5-2 Traditional Rain-fed Agriculture Subsistence Oriented 6-2 Performance of the Traditional Rain-fed Sector 7-2 Historical Background of Agricultural Statistics in Sudan 8-2 Method of Collection Agricultural Data in the Irrigated Sector 9-2 Rain-fed Mechanized Sector
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Chapter Two Rain-fed traditional sector 1-2 Preface: Sudan is endowed with a diversified natural resources base, both renewable and nonrenewable, including vast agricultural land, water and minerals. Oil and gold mining are both have a limited future because these resources are not renewable. However the use of land for traditional rain-fed crop farming and traditional rain-fed livestock production has also been careless and extractive with obvious damage to the natural resources on which these production systems depend. Like oil and gold, the land and forest resources are in danger of being destroyed and exhausted unless their management is substantially improved. Economic growth in Sudan has been driven by oil since 1999. Oil accounted for nearly 40% of domestic revenue and 90% of export earnings and 15% of industrial value added. During this period, agriculture has been on a relative decline in terms of its importance to the Sudanese economy dropping from about 46% of GDP in 1997 to around 30% of GDP in 2011, due to the absolute decline of crop production and productivity. However, the negative trend in agriculture contribution has been partially mitigated by improvement in the traditional livestock production (SDTRA).The country soon faced the consequences of depending on unsustainable production system. This was mainly brought about by the secession of the South in 2011 when 75% of the oil earnings was lost, due to oil fields being in the South. This resulted in the loss of 26 % in overall value added, 90% (12.9% of GDP) loss of exports revenues and 6% of GDP loss in total revenues (SDTRA). In the wake of this worsening economic situation, Sudan was fortunate, that gold revenues relieved some of the pressures on the balance of payments created by the loss of oil revenues and thus averted economic collapse. The sharp increase in gold production accompanied by unprecedented increases in international prices encouraged the government to depend on gold to partially offset the loss of oil revenue. However, by the time Sudan turns to the rain-fed agriculture, assuming the continuity of the present system, natural resources and their productivity may have deteriorated further. 2-2 Traditional Rain-fed Agriculture:The dismal performance of the sector indicates that the contribution of the rain-fed sector is far below its potential. The average growth rate of crops in the sector fell from a solid 24.6 percent in the 1990s to 2.4 percent during the period 2000 to
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2008 basically due to lower yields. In general rapid expansion in the areas cultivated was behind the entire growth of output in rain-fed agriculture whenever it happens rather than yields. Yield of sorghum, the major rain-fed crop increased from 248 kg/feddan during 1990/91-2002/2003 to 259 kg/feddan during 2004/2005-2014/2015. The production of sesame, a predominantly rain- fed crop which has been a dominant export crop in the past, has increased dramatically. Its yearly average yield was increasedfrom an average of 73 kg/feddan during 1990/91-2002/2003 to 100 kg /feddan during 2004/2005-2014/2015. Table (2-1) Area harvested, Production and average yield of Sorghum and Sesame(90/91-2014/2015) Season Sorghum Sesame Havrvested Area Production Yield Havrvested Area Production Yield 1990-1991 6570 1176 179 1104 80 72 1991-1992 11109 3581 322 1280 97 76 1992-1993 14761 4042 274 3208 266 83 1993-1994 11152 1990 178 2931 176 60 1994-1995 15303 3648 238 3206 170 53 1995-1996 12007 2480 207 3586 313 87 1996-1997 15603 4089 262 4427 416 94 1997-1998 12646 2871 227 3766 281 75 1998-1999 15024 4143 276 3766 281 75 1999-2000 10780 2347 218 5382 348 65 2000-2001 10008 2491 249 4477 282 63 2001-2002 13683 4394 321 3780 296 78 2002-2003 12667 2825 223 1866 122 65 Period Average 12409 3083 248 3291 241 73 2003-2004 16867 2663 158 3783 401 106 2004-2005 10079 2678 266 3627 277 76 2005-2006 10505 4327 412 4339 400 92 2006-2007 15655 4999 319 2672 242 91 2007-2008 15753 3869 246 3544 350 99 2008-2009 16293 4320 265 2962 317 107 2009-2010 13364 2630 197 3031 248 82 2010-2011 17341 4605 266 3529 363 103 2011/2012 9559 1882 197 1953 187 96 2012/2013 16991 4524 266 5137 562 109 2013/2014 10372 2249 217 1911 205 107 2014/2015 20944 6169 295 6330 721 114 Period Average 14477 3743 259 3568 356 100 Source: Calculated from Department of Agricultural Statistics Data.
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The way in which business is conducted under the three major sub sectors of rain-fed agriculture (namely; semi mechanized, traditional and nomadic/transhumant livestock) threatens the existence of the whole rain-fed traditional agriculture. Due to lack of secured land ownership (or long term tradable leases) and inadequate inputs, the current managerial practices that are based on a short term perspective, disregard the social costs of damage to the environment. Traditional farmers expand horizontally by increasing area planted to compensate for the low yields. The increasing pressure on land resulting from the increasing number of animals and a withdrawal rate less than the ideal rate, and increased demand for land investment; all these factors led to unprecedented pressure for land uses, locked the livestock routes and weakened their development. Moreover, the secession of South Sudan in turn led to the loss of pasture available for grazing space and locked livestock routes. All attempts to open and expand the stock routes have been met with resistance by local and foreign investors and traditional farmers who found themselves prey to land dispossession process that is regularly widening its circle under the auspices of the government. Semi-mechanized agriculture occupies large parts of the clay plains in the high rainfall savannah belt and has considerably increased from around 8.9 million feddans in 1980-85 to 14.5 million feddans in 2006-2012, extending from Al Fashaga in Eastern Sudan to Southern Kordofan in central Sudan and to South Darfur (Um Ajaj) in the far west. Farm sizes for individuals vary from 500 to 1500 feddan un-demarcated semi-mechanized areas (where land is not surveyed) are more than the demarcated areas (SDTRA). Land is allocated to officials and private investors to produce grains. In this process semi- mechanized farming crowded out traditional small producers, intruded into livestock routes and created conflicts between small traditional farmers, livestock herders and large investors. This production system has left behind millions of feddans of desert. If thispractice continued, then it will only be a matter of time before most parts of the country are turned into a big”Dust Bowl”. Annual dust storms (haboubs) in Khartoum are advance warnings of the complete destruction of the farming system.The traditional rain-fed agriculture has in the past relied on a relatively more sustainable traditional system of rotation and inter-cropping on farms that are typically about 20 feddans on average. This system started to break down since the early seventies due to pressures from drought,
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desertification, population increase, introduction of semi-mechanized agriculture, poor and inefficient transfer of technology and low input use and above all lack of incentives associated with the land tenure system. Demographic, political, and technical challenges are now upsetting this balance. 2-3 Traditional sector: The traditional rain-fed sector is the most important in terms of area cultivated, aggregate production, contribution to food security and livelihood of the rural poor, employment opportunities, provision of raw material to the processing sector and mobilization of the whole economy through its forward and backward linkages. The share of the sector in the country’s Gross Domestic Product (GDP) increased on average from 12.5% during the period 1991/92- 99/2000 to almost 15% during the period 2000-2008. The sector is the main contributor to the country’s non-oil export earnings (livestock, sesame, groundnuts, and Gum Arabic, hibiscus and watermelon seeds). The share of the sector in the total agricultural exports earnings in 2011 was US$550 million representing about 75% (SDTRA). Western Sudan has 91% of the rain-fed area under cultivation (54 % of total area in Greater Kordofan and 37% in Greater Darfur) and rain-fed production in this region constitutes 81% of total rain-fed output (47% in Greater Kordofan and 33% in Greater Darfur) Livestock is the largest subsector of the Sudanese domestic real economy and is a growing contributor to exports. The great bulk of all livestock production – possibly 90% of the total, – comes from small holders and migratory producers (SDTRA). Despite this overwhelming importance of the traditional rain-fed sector, and its potential for growth, food security and poverty reduction, insufficient attention has been paid to and treated as a residual sector in terms of supporting policies and budget allocation for development. 2-4 Contribution of the sector to export value Like most developing countries, Sudan exerts continuous efforts to promote its foreign exchange earnings and to bridge frequent gaps in trade and current account balances. Sector contributions to export earnings gain paramount importance. Export values of the traditional sector have been derived from single commodity export values specific to the sector (including processed vegetable oils) after netting out commodity values that are shared with other sectors (e.g., sesame and groundnuts) in proportion to the amounts produced. Fluctuating as it was, the share of the traditional sector remained relatively high. The sector’s trend value can be derived to
10 show a decreasing annual trend of $10.216 million since 2004 (compared to $25.934 million for the agricultural sector). Most of the deterioration in the sector’s value of exports in later years is attributable to a weakening in the export values of Gum Arabic, ‘karkadeh’ and melon seed in addition to fluctuating exports of sorghum and decreasing returns from camel exports. On the other hand, sesame and sheep exports have witnessed discernible improvements. To conclude, although the share of the sector in total agricultural export earnings remained high, it is more or less stagnant and far away from the potential of the sector (SDTRA). 2-5 Traditional Rain-fed Agriculture Subsistence Oriented Nonetheless it assumes an important role in economic development and poverty reduction in the Sudan, as depicted by the following parameters: 1. Thearea it occupies. 2. The size of the population engaged. 3. Contribution to the food needs of the country. 4. Share in commodity export, and in foreign exchange earnings. It is extensively practiced in both sandy and clay areas, covering most states of Sudan receiving average annual rainfall within ranges of 300 to 400 mm and it coalesces with other forms of production: livestock raising (sedentary and nomadic), and hashab tapping for (Gum Arabic) production. Farming in the rain-fed traditional sector occupies an estimated 24.5 million feddan (10.3 million hectare), representing slightly less than two thirds of the total cultivated area in the country (SDTRA). The sector is vital to the country’s food security and export crops. The sector is the main contributor (57%) in the total area devoted to the five major food crops of sorghum, sesame, millet, groundnuts and wheat (traditional wheat is grown in Jebel Marra). The greater states of Darfur and Kordofan, Blue Nile, Sinnar, and White Nile occupy the most important traditional rain-fed areas. The traditional rain-fed agriculture derives its essence from the many traits describing its existence, as revealed by the following features: 2-6 Performance of the Traditional Rain-fed Sector: The rapidly growing demand for food products and the recurrent food shortages resulted in a serious food production gap. The situation has been exacerbated by the secession of South Sudan and loss of most of oil earnings. These domestic and international variables have induced policy makers of late to recognize the importance of the sector. The traditional rain-fed farming
11 areas that produce a wide variety of products recorded the largest decline in performance. 2- 7Historical background of agricultural statistics in Sudan:- Agricultural data collection in the agricultural sector started as early as the beginning of the 20th century, with the establishment of department of agriculture and veterinary services, followed by department of irrigation. The department of statistics evolved as a division in 1903 and developed into department in 1953 & into a central bureau of statistics in the late 80s. The first agricultural economics and statistics section within the ministry of agriculture was established in 1958. It started with a very limited numbers of officials with economic and agricultural background. In the early 60s, the division received a technical support in the field of agricultural statistics, and international expert was employed to assist the division to develop and adopt objective methods of data collection, analysis and publication. Theoretical and practical training courses were conducted in area measurement and crop cutting experiments. Sudan in considerate are of the very early countries in Africa and the Arab countries with applied crop cutting experiment to estimate yield of sorghum. The first specialized agricultural statistics bulletin was published 1960/1961, containing information on area, production and average yield of the main crops by centre of production, administrative set up and type of irrigation. Also rain fall data was included in this bulletin. This series of annual bulletins continued till 1969/1970. In 1970/1971, it was substituted by the agricultural your book, which was on the same line as the bulletin, but included more detailed information of the main crops, rainfall and some livestock data,. In mid 80s other publications were issued as the current agricultural statistics bulletin (CAS) and agricultural situation and outlook. These publications were meant to give supplemented information to data included in the yearbook or to bridge the gap between two successive issues of the agricultural yearbook. Since the late 80s and animals the only the publication issued by the admin of agricultural statistics admin is the agricultural statistics and outlook. The agricultural division was up graded to administration of agricultural economics and statistics, under the umbrella of the general administration of agricultural planning and economics. During the period 1990/1991 the administration received financial and technical support through the agricultural planning and statistics project financial by USAID. The administration benefited from the project in building capacities in form of training at all
12 levels and a formof equipment and transport facilities. Also this period witnessed advanced trials for constructing an area sampling frame. In 1993, the agricultural statistics got autonomies status as evolved as our independent administration. On 1996 within the new structural set up in the ministry of agriculture, a general admin of information and statistics was established comprising three administrations, namely agricultural statistics, computer and documentation and agricultural economics. But in 2001, due to the institutional reform undertaken by the ministry of agriculture, the agricultural statistics administration again reformed to the general directorate of planning. After the implementation of the federal system in Sudan, data collection, analysis and publication was entrusted to the state ministries of agriculture, while the national agricultural schemes(Gezira, Rahad, New Halfa and Suki) were responsible for producing their own agricultural data. The role of agricultural statistics at the federal level was confined to training, technical support, co-ordination and publication of the agricultural data at the country level. Methods of collecting current agricultural statistics: As methods of data collection may differ from agricultural sector to another it is better to have an idea about the different agricultural sectors in the country. According to type of irrigation, agriculture in Sudan can be divided into two main sectors: The irrigated sector: This sector includes areas irrigated from the River Nile and its attributers by pumps, or gravity or flood even from seasonal streams other than the River Nile. Also areas irrigated by pumps from bore (Mataras) are considered as a part of this sector. Rain fed sector: In this sector the source of irrigation is rains. The rain fed sector is further sub divided into mechanized rain fed sector which is categorized by using machinery land preparation and harvest whether fully or partially and also large size of holdings is a category of this sub sector. A sizable portion of the mechanized sector is demarcated into schemes of regular shape of 1000 and 1500feddans.Part of this sub sector is un-demarcated and the size of holding can range from less than 100feddans to a few thousands (up to 5000). The other sub sector is thetraditional rain fed sector. This category includes areas mainly in western and
13 southern Sudan where no machinery is applied and traditional methods of cultivation (agric. tools) are adopted, but besides this, small holdings(roughly up to50feddans) while use machinery in land preparation and partial harvest are considered as part of the traditional sector. 2-8 Methods of collection agricultural data in the irrigated sector: National schemes: The national schemes follow a proper crop rotation, where each crop is planted in a separate piece of land known as number with a definite size of feddanage and usually includes tenancies with equal sizes. Also the lay-out of the canalization system facilitates the estimation of planted areas under each crop. Accordingly, the statistics of area planted are accurate and reliable. The estimation of yield is based on sample survey were crop-cutting is conducted, an example is Gazira scheme, the statistics division of the agricultural planning administration carries an annual survey to estimate yields of the main crops (sorghum, wheat, groundnuts and cotton). As the administration is interested to have information at the level of the block, all blocks are included, as the first stage of selection starts at the tenancy level. In scheme, 36 tenancies were selected from each block resulting 3.2% according for the planted area, in a sample size of 40032 tenancies. The sample design adopted is a multi-stage random sample. In the first stage applying systematic random selection, three canals (Turaa) are selected from each block, representing the start, the middle and the tail of the major canal. In the second stage, from each selected canal three numbers are selected applying simple systematic random selection, also representing the start, the middle and the tail of each number. At the 3rd stage, 3farmers are randomly selected from each selected number, one at the start, one at the middle and one at the tail. At the last stage, 3plots of 2*2 meters are randomly selected at the beginning, the middle and the end of the tenancy. Then the heads are cut dried, threshed and weighted, and the weighted average is calculated to estimate the yield of crop. All the same time paroled estimation which is mainly base on weekly records of the agricultural inspectors is prepared by the agricultural administration. Both estimates are mode available to the top administration. Of the scheme I think so as to avoid duplication and sometimes contradiction, it is better to depend on the objective method adopted by the planning administration and tosupply with more facilities and financial capabilities to improve this
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job. The other national schemes (Rahad, New Halfa, Suki) are using more or less similar procedures of estimation, but Gezira scheme is more experienced in the aspect and its coverage and persistence is better. Other irrigated agricultural schemes: The state ministries of agriculture are responsible for generating the agricultural statistics of the irrigated sector in that state. Although these schemes are having their own agricultural rotation and somewhat similar canalization like the national scheme, but they rarely follow objective method of estimation. The data of area planted and area harvested as fairly good degree of accuracy, and as usually there is a plan for targeted area and a close follow up at area planted and areas to be harvested. An early stage where crops are at maturing stage yields depend on eye estimates, and then refined from acetous records of threshers or combine harvesters at harvest time as crops like sorghum, wheat, broad bean are harvested either fully or partially by combine harvesters or threshers. The accuracy of yield figures in this sub sector can be considered acceptable, as an example we will considered this procedure adopted for collecting agricultural data mainly for food crops in River Nile state. According to the administrative division in the state, they are six localities, at each locality there is an agricultural inspector, assisted by new graduates of agriculture, who are located at administrative unites under the locality. Each locality has an average of about 10basic units. Each assistant inspector is responsible to collect data from their units by interviewing farmers plus his own observations, weekly reports are submitted from each locality from the time land preparation till the time of harvest, giving information about areas, performance of the crop yields and factor affecting the crop type, rain fall, number of irrigation, application of fertilizer, number of weeding, pests, and diseases etc …. At time of harvest, the inspectors try to record the production by following the combine harvester's threshers in the field. The agricultural planning administration within the ministry of agriculture at River Nile state is responsible to prepare a weekly report reflecting the agricultural station at state level. 2-9 Rain- fed mechanized sector: Estimation of planted area: The preliminary estimates of area depend to a large exert on the records of the annual renewal of the schemes as the farmers are supposed to pay laud rent before the start ofthe season. This information is supplemented and refined information of rain fall, prices, and information from
15 farmers. Usually in September team from mechanized farms co-operation (MFC) tour all schemes from door to door to estimate the planted area either by interviewing the farmers or the manager of the scheme or by eye estimation by the members of the team. In November and December, depending on the availability of funds and transportation facilities, the teams estimate the areas to be harvested and the expected yield by subjective methods (eye estimation).The federal administration of agricultural statistics of the ministry of agriculture in calibration with state ministries of agriculture used to carry crop cutting surveys to estimate the yield of sorghum. The intensity of coverage and timeliness of these surveys depend considerably on the availability of financial resources. The coverage of the surveys in season05/2006 was the best during the last 15 years as it covered Gedaref, Damazin, S.Kordofan, Sennar, White Nile and Gedaref being the largest area is chosen as an example to explain the sampling procedure of the crop cutting survey.
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CHAPTER THREE – Literature review
1-3 Preface 2-3 Survey sampling 3-3 Observational access to the population 4-3 Important and desirable properties of a frame 5-3 Simple random sampling 6-3 Stratified sampling 7-3 Cluster Sampling 8-3 Systematic Sampling 9-3 Estimating the Variance 10-3 Non-sampling Error 11-3 Agricultural Surveys 12-3 Measurement of Estimator Quality 13-3 Standard Deviations 14-3 Standard Errors 15-3 Coefficient of Variation 16-3 The Estimation of the Production 17-3 Some Sampling Surveys in Sudan 18-3 Rain-fed Mechanized Sector 19-3 Some Surveys in Egypt and India 20-3 Research Type 21-3 Assessment Methodology 22-3 Multiple Comparison of the Means Procedure
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Chapter Three Literature Review 1-3Preface: Broadly sampling stand for selection of a part of [ sample] from some whole [population] observing selected part with respect to some property of interest and then drawing some conclusion [inference]about the whole (Tore Dalenius 1985) . Sampling is used as a mean of attaining knowledge in two ways: sampling in everyday life: For example a housewife tastes a spoonful of soup to see the level of salt, a physician draws a few milliliters of blood from a patient to determine the ratio of white cells to red cells and an archaeologist excavates an ancient burial ground to find some objects to form an opinion about the culture which produce these objects. Statistical sampling: It is also called scientific sampling. It denotes selection of a sample from some population observing that sample with respect to some property of interest, and making inference about the population, throughout using procedures based on statistical theory. Statistical sampling is used in different areas, as an examples, experiments and survey sampling. The difference is that, experiment is carried out to measure the effect of treatments, and the study is said to be based on experimental data, while survey sampling is based on observational data as generated by nature. This difference is of decisive importance with respect to the validity of inference. 2-3Survey Sampling: There is no accepted definition of survey, and hence survey sampling, many definitions of survey is written, but the most two often quoted definitions are: 1- An examination of an aggregate units, usually human beings or economic or social institutions. Strictly speaking perhaps "survey should relate to the whole population
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under consideration but it is often used to denote a sample survey i.e., an examination of a sample in order to draw conclusions about the whole" 2- "Many research problems require the systematic collection of data from population or samples of populations through the use of personal interviews or other data gathering devices. These studies are usually called Surveys, especially when they are concerned with large or widely dispersed groups of people" Classes of Survey Populations: Three classes of populations are identified as objects of survey sampling, the first is the process in the plane, the plane may be total land of a country, and the process may be biological. Secondly, a process in time, the time may be a calendar year, and the process may be births and deaths. Thirdly, a finite set of objects of some kind, such as individuals. The Necessary Basis for Survey Sampling: Sampling survey must be measureable and control the uncertainty of the estimates, and sampling survey design must meet certain efficiency conditions; it must accommodate cost- reducing procedure for data collection and control various sources of non-sampling errors. The development of new methods and theory of survey sampling make it feasible to meet the above mentioned conditions. Bases for planning a Sample Survey: The decision: The decision to consider statistical study, there must be a problem or group of problems to the solution of which the study is expected to contribute. Such a problem is called a user's problem, which is to be well understood by the user as well as by statistician who is to be in charge of the statistical study. Once the user's problem has been carefully formulated, the next step is to translate it into a statistical problem, to provide the information the user needs as a basis for tackling the problem. So, the decision is made to plan a sample survey. The population of interest: The information needed for tackling the user's problem concern a finite set of individually identifiable objects, which are refer to as elements and a set of elements refer to as a population. The information of interest:
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Sample surveys are used to provide estimate of numerical characteristics describing the population of interest. For each one of several properties, there is specific measurement procedure, which may apply in a uniform manner to all elements in the population. This would generate data, represent by data matrix with one column for each element. The data matrix is typically a conceptual entity, defined with reference to the measurement procedures. The needed accuracy of the estimate: The uses to be made of the estimates determined the necessary accuracy of the estimates. ŷ is an approximation of Ŷ. So the users naturally expect, ŷ to be a good approximation. Such an approximation must, however be started more precisely. If the users prime consideration is that ŷ is sufficiently close to Ŷ; regardless it is under or over estimate, then the needed accuracy may be then expressed as follows: The error of the estimate must be less than [plus or minus a critical value ά, specified in advance of making the survey. In other hand if the user are concerned about the direction of the error; an under estimate by a certain amount may be more serious than an equally large estimate. Then the needed accuracy may be expressed as above but more detailed. Criteria for Survey Sampling: The statistician in search for survey sampling to be adopted uses some means which help to focus on good design. An important class of such means is criteria for survey sampling. The Measurability Criterion: Measurability should be a distinct criterion, rather than one to be included in the definition of probability sampling and second in importance to probability selection, add to that the measurability of complex samples need codes for ultimate clusters and strata (Steven Heeringa& Graham Kalton 2003). To provide estimate having the needed accuracy, it must be possible to measure how well the estimates approximate the corresponding parameters. The measure needs not to be exact; it may be in the nature of an approximation. Themeasurability is to be achieved by means of probability sampling; this means that the elements selected for a survey must be selected with known probabilities. This criterion is supplemented by the pre-requite that the design be reasonably self-contained [possible to measure the accuracy on the basis of the survey itself, the design and data] without to resort to strong assumption about the population. The Efficiency Criterion:
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The efficiency calls for a reasoned balance between the accuracy of the estimates aimed at, and the cost of achieving that accuracy. This means that the design should yield estimates of maximum accuracy for a fixed cost or required accuracy at minimum cost. The Simplicity Criterion: This Criterion calls for using a design which is simple enough to be carried out in a way faithful to the design. 3-3 Observational Accesses to the Population: Preparing Sampling Frame: Efficiency Considerations: Sample survey means creating some means of getting observational accesses to the population of elements, for short a sampling frame. The data collection would call for observing the sample elements with respect to the properties of interest and possibly also some supervision to assure the accuracy of the data collected. This would be prohibitively inefficient on grounds of the cost of creating the frame and the cost of data collection. The cost of preparing a sampling frame: Instead of preparing a list of the N individual elements of the population O we may prepare a list of M identifiable units of some other, to be denoted by:
[UI| I = 1… M] = [U1… UI… UM] ………….. [1-3] Where M< N, M = N or M > N, as the case may be. When there is no need to specify the individual units, we will denote this set by (U), in analogy with use of (O) to denote the population of elements. (U) must be such that there is association between the M units in (U) and the N elements in (O). It is this association which provides the observational access to (O) through (U); a sample of elements may be selected from (O) by selecting a sample of units from (U). Hence these units will be referred to as sampling units and (U) will be referred to as a sampling frame. The cost of preparing (U) may be muchsmaller than the cost of making a list of elements in (O). We will denote the cost of preparing (U)
by CU. The cost of data collection: This cost will reflect the spatial distribution of the elements selected for the survey; and this in turn depend on the spatial distribution of the sampling units selected: if the elements selected are scattered over a large area, the cost of field work will be higher
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than if the elements are located in a possibly small number of administrative units. We
will denote the cost of data collection by CD. General function: The general cost function for getting observational access to the population suggested as follow:
C = CU + CD…………[2-3] This simple cost function plays a key role in the choice of sampling system. Four basic rules of association: To present the four rules of association we will consider the following situation. Thus there is a population of N elements: (O) = (O1… OJ… ON), and a frame with M sampling units:
(U) = (U1… UI… UM). Basic rule No. 1:One-to-One: Each unit in (U) is associated with one and only one element in (O) and every element in (O) is associated with one and only one unit in (U); hence M = N.
Rule No.1 may be symbolized by: UJ OJ, J = 1… N. Example: The population of elements consists of all inhabitants in a country. (U) is a list of these inhabitants, say population register. Basic rule No. 2: Many-to-One: Each unit in (U) is associated with one and only one element in (O), but an element in (O) may be associated with more than one unit in (U). In this case we denote the frame by:
(U) = (U1… UI… UM) with M>N Rule No. 2 may be symbolized by:
UI-1
UI OJ I = 1... M
UI+1
The rule implies that the OJ is selected if UI-1 or UI or UI+1 is selected. Example: The population of elements consists of all households in a city and (U) is a list of all members of these households. Basic rule No. 3 One-to-Many: Each unit in (U) is associated with several elements in (O); no element is associated with more than one unit in (U).
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The frame is denoted by (U) = (U1… UI… UM), With M < N. th The units in (U) are typically referred to a cluster. The i unit is a cluster of NI elements, I =1..M Rule No. 3 may be symbolized by:
OJ-1
UI OJ
OJ+1 , Where one unit is associated with a cluster comprising three elements. Example: Population of elements consists of all frames in a country, while (U) is a list of administrative units, into which the country is divided. Basic rule No, 4: Many-to-Many: This rule – the basis for network sampling, may be symbolized by:
OJ-1
UG
OJ
OK
UJ
OK+1 We will not elaborate on this rule; it is merely presented here for making the list of rules complete. An Important distinction: As a preliminary to the discussion of important and desirable properties of frame, we will introduce the distinction between the target population of elements and the sampled population of elements. The target population: This is the population of elements which we want to investigate by means of a sample survey. It may be symbolized by (O) T. The sampled population: This is a population of elements, to which we have observational access by means of frame. It may be symbolized (O) S.
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Sampled population
Target population
It is important to realize that the sampled population often is not identical with the target population as shown in the above figure. 4-3Important and desirable properties of a frame: The frame construction must be tackled in a way that reflects the survey situation with respect to the following aspects: 1: The kind of population of elements. 2: The geographic distribution of the target population. 3: The survey operation to be carried out, and notably the data collection. In order to arrive at a good solution to the problem of frame construction, it is helpful to consider the technical properties in term of which alternative frames may be assessed. These properties cover important properties and desirable properties. Important properties: 1: The frame must make it possible to compute estimates concerning a population of elements (complete).
2: The frame must serve to yield a sample of elements, which can be unambiguously identified. 3: The frame must be such that it is impossible to determine how the units in the frame are associated with the elements in the (sampled) population. Desirable properties: 1: The frame should be simple to use. 2: The frame must be organized in a systematic fashion, as an example, units in (U) may be ordered by geography or size. 3: The frame includes auxiliary information. 4: The frame should be reasonable stable in time. Techniques for frame construction:
There are two types of fames to be considered, list frame (directory
24 type) and lists in the form of processed maps (map type).For directory type the general format is a list, and for the map type the general format is a map of some area which has been divided into (non-overlapping) smaller areas, which serve as sampling units.
Three special problems are to be considered: 1: The problem of multiple lists, this problem arises when there are two lists of elements; the rule of association is one-to-one in both cases. Some elements are on both lists; other elements, however, are on only one of the lists. The fact that some elements may be accessed by means of both lists is a problem which has to be addressed. Three options are to be considered, first one calls for eliminating from one of the list those elements which are on the other list. The second option calls for select samples independently from list number one and list number two. Then delete from the sample from list number two any element, which is also a member of list number one. The last and the third option calls for selection of two independent samples one from each list. When computing estimates, we must take into account that some elements in the population have probabilities of being selected which reflect this situation. 2: The problem of empty units, this problem occur when there is one or more units in (U), not associated with an element in (O). The population of elements may be the families in a city as of today. (U) is a list of dwelling units in that city. For some of the dwelling units in (U), it holds true that no elements are associated with them; we will say that these units are empty. 3: The problem of incomplete lists, for some populations, a list of the elements may be available, but this list is incomplete; it does not comprise all elements in the population. Survey Sampling: Survey sampling is the process of selecting a probability-based sample from a finite population according to a sample design. You then collect data from these selected units and use them to estimate characteristics of the entire population. A sample design encompasses the rules and operations by which you select sampling units from the population and the computation of sample statistics, which are estimates of the population values of interest. The drawing of random samples cannotbe left to subjective discretion but must be the result of objective and preferable mathematical methods (Robert G.
25
D. Steel & James H. Torrie 1981).The objective of your survey often determines appropriate sample designs and valid data collection methodology. A complex sample design often includes stratification, clustering, multiple stages of selection, and unequal weighting. There are two types of sampling are to be distinguished, the probability sampling and non-probability sampling. A probability sampling is one in which every unit in the population has a chance (greater than zero) of being selected in the sample, and this probability can be accurately determined. The combination of these traits makes it possible to produce unbiased estimates of population totals, by weighting sampled units according to their probability of selection. Non-probability sampling is any sampling method where some elements of the population have no chance of selection (these are sometimes referred to as 'out of coverage'/ 'under covered'), or where the probability of selection can't be accurately determined. It involves the selection of elements based on assumptions regarding the population of interest, which forms the criteria for selection. Hence, because the selection of elements is nonrandom, non-probability sampling does not allow the estimation of sampling errors. Sampling Systems: There are three basic systems, which are element sampling, cluster sampling and multi-stage sampling. In specific application, one of these systems or possibly a combination of them will be chosen as the sampling system on the basis of the kind of efficiency considerations. Element sampling: This term denotes sampling from a frame (U) which is associated with the population of elements (O) according to basic rule No. 1: one-to-one and basic rule No. 2: many- to-one. Under element sampling come simple random sampling, stratified sampling and sampling with unequal probabilities of selection. 5-3Simple Random Sampling: Simple random sampling is a method of selecting n units out of N such that every one of the N C n distinct samples has an equal chance of being drawn (William G. Cochran 1977). The theory dates back more than a century. It plays a minor role in applications. The reason for its nonetheless prominent place in account of theory of survey sampling is that SRS allows a simple, yet informative discussion of some important topics. The rule of association is one-to-one. With each element we associate Y-,X-,and A- data. A number of parameter is to be defining for these data, expressed in term of the Y-, X- and A- data, respectively.
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Y- parameters: The mean per element, we write as:
1
The total we write Ŷ as = T -Y ∑= N.ŶYJ …………... [3-3] N The population variance among the Y- data is:
1 2 2 Simple random sampling is usedσ = with ∑ reference (YJ – Ŷ) to ………[ two sampling4-3] schemes, namely sampling N without replacement and sampling with replacement. SRS without replacement: The sample is selected at random from (U) in n consecutive draws: At the first draw, each element has a probability 1/N of being selected. The element is not replaced into (U). In the second draw each remaining element has a probability 1/ (N-1) of being selected. Again, the element is not replaced into (U). This procedure is continued until n elements have been selected. The outcome is a sample of n distinct elements which may be represented by:
{Oj | j = 1…n} = {O1… Oj… On}
The use of lower case ,j, for the index signifies that Ojis the jth element selected for the sample, to be distinguished from OJ which is the Jth element in the population. The corresponding different combinations of n elements out of N, is: 푁! 퐶푁 = … … … . . [5 − 3] 푛 (푁 − 푛)! 푛! 푁 푁 Each of these 퐶 푛 samples has thesame probability 1/퐶 푛 of being selected. This mechanism is obliviouslynot practical. Two alternative mechanisms of practical interest are to be identified (Tore Dalenius 1985) . Alternative mechanism No.1: This makes use of a table of random numbers for selecting n elements from a population of N elements. Alternative mechanism No. 2: If the population of elements is ordered at random (thoroughly mixed) a random sample of n elements may be selected by: I: Selecting the n first elements in the sequence. II: Selecting every Kth element from a random start, this is properly referred to as systematic sampling. SRS with replacement:
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In this case, n draws are made from (U); after each draw, and hence before the next draw; the selected element is replaced into (U). The sampling may make use of a table of random numbers. The Estimation of Sample Size: In planning of a sample survey a decision must be made about the size of the sample. The decision is important. Too large a sample implies a waste of resources, and too small a sample diminishes the utility of the results. The decision cannot always be made satisfactory; often we do not possess enough information to be sure that our choices of sample size are the best one. Sampling theory provides a framework within which to think intelligently about the problem. We cannot absolutely guarantee accuracy within 5% except by measuring everyone. To make a rough of n the fpc (finite population correction) is ignored, and the sample percentage p is assumed to be normally distributed. In technical terms, p is to lie in the range (P ± 5), except for a 1 in20 chance. Since p is assumed normally distributed about P, it will lie in the range (P ±
2σp), apart from a 1 in 20 chance. Furthermore,
휎푝 = √푃푄/푛 … … . . [6 − 3] 4푃푄 Hence, we may put 2√푃푄/푛 = 5 or 푛 = … … … . [7 − 3] 25 At this point a difficulty appears that is common to all problems in the estimation of sample size. A formula for n has been obtained, but n depends on some property of the population that is to be sampled (William G. Cochran 1977). 6-3 Stratified Sampling: In statistical surveys, when subpopulations within an overall population vary, it is advantageous to sample each subpopulation (stratum) independently. Stratification is the process of dividing members of the population into homogeneous subgroups before sampling. These subpopulations are non-over-lapping, and together they comprise the whole of the population, so that
N1 + N2 + … + NL = N. …… [8-3] (William G. Cochran 1977). The strata should be mutually exclusive: every element in the population must be assigned to only one stratum. The strata should also be collectively exhaustive: no population element can be excluded. So, we can say stratified sampling is another example of a classical sampling scheme and the theory was developed almost a century ago. Stratified poses four design problems:
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1: Stratification variables. 2: The number L of strata. 3: The mode of stratification that is how to group the elements into the L strata. 4: The sample sizes in the strata that is the sample allocation problem. Due to the importance of the sample allocation problem, the focus will be on this problem.
The stratified sample allocation problem: The population of N elements, (O), is grouped into L mutually exclusive subpopulations, called strata with NH elements in the Hth stratum, H = 1…..L. For each stratum, there is a stratum frame (UH), the units of which are the elements; hence the rule of association is one-to-one. The population mean per element is:
1 1 푌̅ = ∑ ∑ 푌 = ∑ 푁 푌̅ ∑ 푊 푌̅ … … . . [9 − 3] 푁 퐻퐽 푁 퐻 퐻= 퐻 퐻 퐻 퐽 퐻 퐻 Where WH = NH/N. The population variance is:
휎2 = 1 ∑ ∑(푌 − 푌̅)2 = 1 ∑ ∑ 푌 − 푌̅ + 푌̅ − 푌̅)2 … … . . [10 − 3] 푌 푁 퐻퐽 푁 퐻퐽 퐻 퐻 퐻 퐽 퐻 퐽
=
… … … [11 − 3]
2 ̅ ̅ 2 = ∑퐻 푊퐻휎퐻푌 + ∑퐻 푊퐻(푌퐻 − 푌) … … . . [12 − 3] = Within stratum variance + between stratum variance There are two assumptions in discussing the theory of different sample allocations. Assumption one: The sample selection from each stratum is carried out by SRS. Both sampling with replacement and without replacement are to be considered. Assumption two: The sample selection from any stratum is independent of that from any other stratum. This will allow us to apply simple theory for linear combination of estimator for the different strata.
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Stratified sampling theory: In stratification sampling there are special theories adopted in sampling.
Proportional allocation: This theory calls for making nH proportional to NH. This may be written as: 푛 = 푁퐻 푛 = 푊 푛 ……… [13-3] 퐻 푁 퐻 The sample is representative of the population, in the sense that nH/n = NH/N ……… [14-3] For proportional allocation the estimator:
̅ ̅ 푌 = ∑퐻 푊퐻푌퐻 ………. [15-3] Simplifies to:
푌̅ = 1 ∑ ∑ 푌 … … [16 − 3]. 푛 퐻 푗 퐻 This means the sample is self weighted For sampling without replacement: 2 ̅ 2 2 ̅ 휎 (푌) = ∑퐻 푊퐻 휎 (푌퐻) ………. [17-3] Becomes: 2 ̅ 2 푁퐻−푛퐻 1 2 휎 (푌) = ∑퐻 푊퐻 . 휎퐻푌 … … … . [18 − 3] 푁퐻− 1 푊퐻
1 푁 − 푛 2 ̅ 퐻 퐻 2 휎 (푌) = ∑ 푊퐻 . 휎퐻푌 … … … [19 − 3] 푛 푁퐻 − 1 퐻
While for sampling replacement the variance becomes: 2 ̅ 2 1 2 휎 (푌) = ∑퐻 푊퐻 . 휎퐻푌 ……….. [20-3] 푊퐻푛
휎2(푌̅) = 1 ∑ 푊 휎2 ……… [21-3] 푛 퐻 퐻 퐻푌 When comparing this variance with the variance when using SRS with replacement from a population which is not stratified, in that case: 푌̅ = 1 ∑ 푌 ……. [22-3] 푛 푗 푗 Has the variance: Var푌̅ =1 휎2 ……….. [23-3] 푛 푌 2 Which, if 휎푌 is expressed as in above, becomes: 1 Var. 푌̅ = [∑ 푊 휎2 + ∑ 푊 (푌̅ − 푌̅)2 ] ……….. [24-3] 푛 퐻 퐻 퐻푌 퐻 퐻 퐻 This expression shows that the gain (= reduction of variance) from using stratified sampling with proportional allocation is: 30
1 퐺 = ∑ 푊 (푌̅ − 푌̅)2 … … … . [25 − 3] 푛 퐻 퐻 퐻 ̅ In general, G> 0; G would be zero, if all stratum means (푌퐻) were equal.
Optimum allocation: Optimum allocation is used for two different but related ways of allocation, namely minimum variance allocation and optimum allocation proper. Here are present for the case of sampling with replacement, and estimating (푌̅) by:
̅ ̅ 푦 = ∑ 푊퐻푦퐻 … … . [26 − 3] 퐻 Minimum variance allocation: Gains from using stratified sampling may be especially large if large sampling fractions nH/n = NH/N are used in strata with large stratum variances, and small sampling fractions are used in strata with small stratum variances. If nH is made proportional to the product of 푊퐻 and 휎퐻푌 The variance 휎2(푦̅) becomes a minimum for a fixed sample size; the variance is:
휎2(푦̅) = 1 [∑ 푊 휎 ]……… [27-3] 푛 퐻 퐻 퐻푌 While the sample is not self-weighted and hence not "representative", the estimator (푦̅) yields a more representative estimate than proportional allocation. The gain from using minimum variance allocation is especially large, when sampling from highly skewed populations, that is populations which comprise a small number of elements which contribute heavily to the total TY, and hence a heavy impact on(푌̅). Optimum allocation proper:
This allocation takes into account three quantities: WH, 휎퐻푌 and the cost CH of collecting the data. Assuming the following simple cost function:
퐶 = ∑퐻 퐶퐻푛퐻 …….. [28-3]
Where CH is the cost per element included in the sample from the Hth stratum, and assuming the total cost of collecting the data is fixed to be C0. Then the optimum allocation proper calls for making
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푊퐻휎퐻 푛퐻~ …….. [29-3] √퐶퐻 Which is allocation minimizes the variance휎2(푦̅). Probabilities of selection: While for SRS and also for stratified sampling using proportional allocation, every element in the population has the same probability of being selected for the sample, this does not hold true for stratified sampling using minimum variance allocation( except for the case where
휎퐼푌= … = 휎퐻푌= … = 휎퐿푌) nor for stratified sampling using optimum allocation proper (except for the case where 휎퐼푌= … = 휎퐻푌= … = 휎퐿푌and CI = …… = CH = …… = CL ). The probabilities of being selected for the sample differ between the strata: there are typically L classes of probabilities of selection, which are unequal among themselves. Post-stratified sampling:
There is stratum frame for stratum (UH). If this condition is not justified, but the stratum sizes WH, H = 1……L, are known the following approach may be considered; - A sample is selected by simple random sampling without replacement. - These elements are observed with respect to the Y-property and also their respective stratum affiliations; assuming that the number of elements selected from the Hth stratum is nH> 0 – if no element has been selected from the some stratum, this stratum is merged with an adjacent stratum; ̅ - For each stratum, 푌퐻 is estimated by 푦̅퐻. - Finally, (푌̅) is estimated by: ̅ ∑ ̅ 푦 = 퐻 푊퐻푦퐻 …….. [30-3] In situations where stratified sampling with proportional allocation performs well, post- stratified sampling may be expected to perform better. Two- phase sampling: The use of two-phase sampling for the purpose of using stratified in a situation where there is no stratification information available about the elements, prior to sample selection. Phase No. 1: A large sample of elements is selected and observed with respect Z, stratification variable. The selected elements are grouped into L strata. The sizes of these strata are estimated by WH, H = 1…….L. Phase No. 2: these calls for selecting samples from each stratum and collecting the Y-data
32
Finally, (푌̅) is estimated by:
ŷ = ∑ 푊퐻 푦̅퐻 … … . . [31 − 3] 퐻
Where푦̅퐻, H = 1……. L, is based on the second-phase sample. Two phase sampling for stratification is efficient in a situation, where the cost of collecting the Z-data is low, and at the same time, the gain from using stratified sampling is large. Cut-off sampling:
Cut-off sampling is occasionally used to estimate a total TY for a markedlyskew population. The choice of stratification variables: The elements in (O) are to be grouped into strata on the basis of the values of a specific stratification variable Z, to distinguish it from the estimation variables Y and X. If one set is comprised by qualitative data and the other set by quantitative data, it is advantageous to use the qualitative data for stratification and the quantitative data for estimation. The number L of strata:
The variance VarL(푦̅) when using L strata, may be expected to be smaller than the variance VarL-1(푦̅) when using L-1 strata. The gain from increasing the number of strata from L-1 to L will in practice, be a decreasing function of L in the context of element sampling. A few well chosen strata will produce a gain close to the maximum gain possible The mode of stratification: For the stratification variable Z, the range of Z has to be partitioned into L intervals (strata) by points:
Z0 < Z1< ……..< ZH <……..< L-1 < L, no Z-value is larger than ZL The strata should be internally homogeneous as possible: the within strata variances should be small. Sampling with unequal probabilities of selection: The idea here is the same as in stratified sampling using optimum allocation; the probabilities of selection are unequal to all N elements. For population of N elements ((O) =
(O1,…,OJ, …,ON)) and a frame of (U), the rule of association is One-to-One. With these elements we associate Y- and n-values which are subject to the following conditions in preparation for developing the sample selection plan:
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O ∑퐽 푛퐽 = 1 ………. [32-3] These n-values will serve as the basis of sampling schemes. The sampling scheme calls for making n draws with replacement, using the n-values as the probabilities of selection. The procedure of making a draw may use a table with cumulative n-values and a table of random numbers. 7-3 Cluster Sampling: There are two main reasons for application of cluster sampling, first no reliable list of elements in the population is available and that it would be expensive to construct such a list. Secondly there are no complete and up-to-date lists (William G. Cochran 1977). Cluster of Unequal sizes: Cluster comprises different numbers of elements. For a frame (U), the units of which are clusters; the rule of association is One-to-Many. The clusters may be compact, that is clusters are made up of contiguous elements, as an example a block in a city, the elements being households residing there; or non-compact, that is cluster made up of non-contiguous elements, as an example the elements numbered 1, 12, 21, ….. in a list of elements, such as a directory of retail stores. The population and the parameters: The population (O) of elements is grouped into M clusters, the set of which constitutes the frame: (U) = (U1,…,UI,….., UM). The different elements in each M reflect the fact that the clusters are of unequal sizes. The cluster totals: T1,….,TI,….., TM Where 푇퐼 = ∑퐽 푌퐼퐽 ………… [33-3] The overall total: 푇 = ∑퐼 푌퐼 ……… [34-3] The mean of the cluster totals: 34 1 푇̅ = ∑ 푇 ……….. [35-3] 푀 퐼 퐼 The mean number of elements per cluster: 1 푁̅ = ∑ 푁 ……… [36-3] 푀 퐼 퐼 The means per element within clusters: ̅̅̅̅ ̅̅̅ ̅̅̅̅ 푌1, … , 푌퐼 … . , 푌푀 … … . . [37 − 3] ̅̅̅ Where 푌퐼 = TI/NI ……. [38-3] The overall mean per element: 푇 1 1 푌̅ = = ∑ 푇 = 푀푇̅ ……… [39-3] 푁 푁 퐼 퐼 푁 The population variance: 1 1 휎2 = ∑ ∑ (푌 − 푌̅ )2 + ∑ 푁 (푌̅ − 푌̅)2 ……….. [40-3] 푌 푁 퐼 퐽 퐼퐽 퐼 푁 퐼 퐼 퐼 The expression for the population variance is equivalent with the corresponding expression for stratified population: 2 1 1 ̅ 2 1 ̅ ̅ 2 휎푌 = ∑퐻 푁퐻 . ∑퐽(푌퐻퐽 − 푌퐻) + ∑퐻 푁퐻(푌퐻 − 푌) ……. [41-3] 푁 푁퐻 푁 = within stratum variance + between stratum variance. A sample of m < M clusters is selected by means of SRS without replacement. Estimation of (푦̅) : Two estimator of overall mean per element to be consider: 푇 1 1 푌̅ = = ∑ 푇 = 푀푇̅ ….. [42-3] 푁 푁 퐼 퐼 푁 Estimator No. 1: This estimator is of the following type: 푌̅ = 1(Estimator of T = 푀푇̅) …. [43-3] 푁 1 1 = . 푀 . ∑ 푇 ……. [44-3] 푁 푚 푖 푖 The variance of (푦̅) is Var(푦̅) = Var {1 . 푀 . 1 ∑ 푇 } …….. [45-3] 푁 푚 푖 푖 which can be written as: 푀−푚 1 1 푁 푣푎푟푌̅ = ∑ [ 1 푌̅ − 푌̅ ̅ ]2 [46-3] 푀−1 푚 푀 퐼 푁̅ 퐼 35 The variance may be large. This occurs when the sizes of clusters vary greatly, and ̅ ̅ hence the factors NI/푁 by which 푌퐼 is multiplied vary greatly. Estimator No. 2: This estimator which calls for estimating both T = 푀푇̅ and N. 1 푒푠푡푖푚푎푡표푟 표푓 푇 푀. ∑ 푇 푌̅̅̅ = = 푚 푖 푖 ………… [47-3] 푟 푒푠푡푖푚푎푡표푟 표푓푁 1 푀.푚 ∑푖 푁푖 which simplified to: ̅̅̅ ∑푖 푇푖 푌푟 = ………. [48-3] ∑푖 푁푖 This is a ratio-type estimator, both the numerator and the denominator is a random variable. Hence, in general, the (푦̅) is biased, but if the correlation between the cluster totals and their sizes is positive, the bias may be negligible. The variance of (푦̅) is approximately: 푀−푚 1 1 푣푎푟푌̅ = ∑ (푁 / 푁̅)2 (푌̅ . 푌̅)2 …… [49-3] 푟 푀−1 푚 푀 퐼 퐻 1 Clusters of Equal sizes: In this case all the clusters are of the same size: N1 = ……= NI ……= NM = N0. Hence N = MN0. The cluster may be compact or non-compact. The population and the Parameters: The population (O) of elements is grouped into M clusters, the set of which constitutes the frame: (U) = (U1,…,UI,…, UM). …….. [50-3] The clusters have the same number of elements The means per element within clusters: ̅̅̅̅ ̅̅̅ ̅̅̅̅ 푌1, … , 푌퐼 … . , 푌푀 Where: ̅̅̅ 푌퐼 = TI/N0. ………. [51-3] The overall mean per element: 푇 1 1 푌̅ = = ∑ 푇 = 푀푇̅ ………… [52-3] 푁 푁 퐼 퐼 푁 The population variance: 1 1 휎2 = ∑ ∑ (푌 − 푌̅ )2 + ∑ 푁 (푌̅ − 푌̅)2 ……… [53-3] 푌 푁 퐼 퐽 퐼퐽 퐼 푁 퐼 퐼 퐼 36 A sample of m < M clusters is selected by means of SRS without replacement, just as in that of unequal sizes. Estimation of (푦̅): We consider the two estimators presented in clusters of unqual sizes. Estimator No. 1: 1 1 푦̅ = ∑푖 푇푖 ……… [54-3] 푁0 푚 1 푀.푚 ∑푖 푇푖 Estimator No. 2:푦̅ = 1 …….... [55-3] 푀.푚 . 푚 .푁0 1 1 푦̅ = ∑푖 푇푖 …….. [56-3] 푁0 푚 This is identical with estimator No. 1. 푀−푚 1 1 푣푎푟푌̅ = ∑ [푦̅ − 푌̅ ̅ ]2 ……. [57-3] 푀−1 푚 푀 퐼 퐼 Which is written as 푀−푚 1 푣푎푟푌̅ = 휎2 ………… [58-3] 푀−1 푚 퐵0 8-3Systematic Sampling: The systematic sampling is scheme for element sampling, in which we selecting every kth element. In other hand the systematic sampling is regard as special case of cluster sampling. The selection of m = 1 cluster from a set of M clusters of equal size (Tore Dalenius 1985). The Population and Parameters: The population and parameters will be identical with those of the clusters of equal sizes. We assume that M = k, as used in every kth element. The sampling scheme: The sampling is done as follows: 1- One of the cluster is selected at random 2- This selected cluster identifies the starting element in the first of the N0 rows. 3- The sample is composed of the starting elements and every kth following element. Estimation of (푦̅): 1 1 푦̅ = ∑푖 푇푖 ……. [59-3] 푁0 푚 In the cluster of equal sizes becomes 1 1 푦̅ = 푇푠 = ∑퐽 푌푠퐽 …….. [60-3] 푁0 푁0 37 And the variance 푀−푚 1 1 푣푎푟푌̅ = ∑ [푦̅ − 푌̅ ̅ ]2 ………. [61-3] 푀−1 푚 푀 퐼 퐼 푀−푚 1 푣푎푟푌̅ = 휎2 ……… [62-3] 푀−1 푚 퐵0 becomes ̅ 2 ……… [63-3] 푣푎푟푌 = 휎퐵0 In terms of intra-class correlation§0, this variance is written as: 2 휎푌 푣푎푟푌̅ = (1 + §0(푁0 − 1) ……… [64-3] 푁0 F1 x F2 2 휎푌 Where: F1 = is the variance of SRS (with replacement) of N0 elements, and F2 is the factor 푁0 reflecting the impact of cluster sampling. Characteristics of Systematic Sampling: Systematic sampling has certain characteristics, which make attractive for applications: 1- Simple to execute the sampling scheme. 2- Simple to check that the execution is faithful to the plan. 3- It describes the sample of elements evenly over the population, which leads to favorable effect on the accuracy of the estimates. For these characteristics, systematic sampling has become widely used in sample surveys. And often used as a selection mechanism in a framework such as stratified sampling. 9-3Estimating the variance: The sample that comprises m = 1 cluster means that it is impossible to estimate the variance on the basis of the data collected. One way to address the problem is to use replications. Thus rather than using one starting element and the skipping interval 1/k, r starting elements are used in combination with the skipping interval 1/rk; this scheme referred to as the Tuckey plan (Tore Dalenius 1985). The mean (푦̅) per element would then be estimated by the pooledestimator 1 푦̅ = ∑ 푦̅ ……. [65-3] 푟 푖 푖 i = 1 ……, r, and variance (푦̅) would be estimated by: 1 1 푦̅ = ∑ (푦̅ − 푦̅)2 …….. [66-3] 푟 푟−1 푖 푖 38 10-3Non-sampling Error: It is sources of error other than the use of sampling will operate. In principle every operation of a survey is a potential source of non-sampling error. These errors can be grouped into three major categories as follows: 1- Error due to non-response. 2- Measurement errors. 3- Processing errors. For two different reasons, non-sampling errors represent problems which have to be addressed in the design and analysis of a survey. 1-Non-sampling errors may account for a major part of the total error in a survey, sometimes much more than the sampling error. 2-It is difficult to measure the error of a survey in the presence of a large contribution from non-sampling errors. Special steps have to be taken to address the problems that non-sampling errors pose. Using sample survey rather than a total survey make it feasible to use measurement, since results of sample survey may be more valuable to the users than the results of a total survey. The size of a survey is of importance for a second reason. Thus if the size is small it may easier to control the sources of non-sampling error than if the size is large. 11-3Agricultural Surveys: Under the estimation theory title a doctrinal body is collected which treats to solve a problem with very simple formulation given a set of observations from reality to guess the value a magnitude has taken is under consideration departing from those observations. Obliviously we have got no access to that magnitude but it has some functional relationship with the obtained observation. If the obtained observation taken from reality have not got any degree of uncertainty , the unknown magnitude would be determined without no error from solving , in favor of that magnitude , the functional relationship mentioned before hard .as many times as the experiment being repeated ,us many time the some value would be obtained , However , the nature do not behave like that ,let repeat any measurement of any magnitude several time and surely different values will be obtained .The functions shall be with higher or lower amplitude depending on the 39 random factors which affect the problem, and thus averaging all those measurements , fluctuation will decrease as the number of averaged measurements increase . 12-3Measurement of estimator quality:- An estimator is a function of the observations, what gives rise that the estimator results in a random available, for that reason, the estimator quality can only are given in probabilistic terms. The quality criticism commonly adopted for a parameter estimator is the minimum mean squared error criticism. Scalar parameter Q, and denoting the estimator with Q^, the achieved error would be equal to E = Q - Q^ and its mean squared error would be, E{E²} = E{ (Q-Q^ )²}. Standard deviation and standard error are perhaps the two least understood statistics commonly shown in data tables. Both statistics are typically shown with the mean of a variable, and in a sense, they both speak about the mean. They are often referred to as the standard deviation of the mean and standard error of the mean. 13-3Standard deviations: It's a measure that summarizes the amount by which every value within dataset varies from the mean. Effectively it indicates how tightly the values in the dataset are bunched around the mean value, It takes account every variable in the dataset. When the values in a dataset are pretty tightly bunched together the standard deviation is small, and vice versa. The standard deviation is usually presented in conjunction with the mean and is measured in the same units. 14-3Standard errors:- It is statistical term that measures the accuracy with which a sample represents a population in statistic, a sample mean deviates from actual mean of the population, this deviation in standard error. The small standard error and more representatives the sample will be over all population. The standard error is also inversely proportional to sample size, the lager sample size, the smaller standard error because the statistic will approach the actual value. 15-3Coefficient of variation: The Coefficient of Variation [CV] also known as” relative variability “equal the standard deviation divided by the mean. C.V is often presented as a given ratio multiplied by 100, C.V for a single variable aims to describe the dispersion of the variable in a way that does not depend on the variables measurement unit, the higher the C.V the greater the dispersion in the variable. The 40 C.V for a model aims todescribe the model fit in the term of the relative size of squared residuals and outcome values, the lower the C.V the smaller the residual relative to the predicated value. 16-3The estimation of the production: Two major factors affecting directly the production estimate, normally the harvested area (productive area) and the yield per area unit. Production = Harvested area x Average yield per area unit. Area Estimation:- Area estimated either by actual form measurement or by Eye estimation accompanied by some techniques to justify the estimation like quantity of seeds sown or number of plowing hours and selection of small sub-sample the from the survey sample to reach a correction factor to minimize error percentage in this estimation. Yield estimation: Many ways used to estimate yield, but the most used are the following: Complete harvest:-This method is summarized in the following:-Selection of random sample from the targeted crop farmers. -The farms of selected farmers are completely harvested. -Determining the total production of the selected sample. -Estimate the yield of the crop by dividing the total production by the total area of the sample. This method theoretically logic but practically and because it depend on complete harvest, it needs time & and for some extend tired some. Due to that it is not practiced, but it good estimation especially in small farm and farmers responded to the enumerators. Sampling Harvest units: - In this method the following steps are used -Selected random sample from farmers of the targeted crop (sorghum). -choose sample from the harvesting units from each selected farmer. -weighed each selected unit, and then estimate the average weight of the harvesting units. -total production is calculated by multiply the average weight of harvesting unit by the total numbers of the units. -The yield is estimated by dividing the total production on the harvested area. Although this method is good but many constrained are found: A-Enumerators must be available at harvesting time of the selected farm. B- Impossible to choose in case of transportation some of harvesting unit from the farm. 41 c- This method not applicable in case of crops that are harvested many times in the same season. -It is clear that this method depend on three factors, normally, the cultivated area, the weight of harvesting unit and number of production units. If this is done accurately, then the yield should be more accurate at farm level. Crop Cutting Survey:- This method is widely used to estimate the yield of the area unit, so it is valid to measure the variation in yield between the different producing centers or the different seasons. It is achieved by selecting random sample from farmers or farms and determined randomly by objective method two plots from each selected farmer. The size of the plots: The size and shape of the plots are given much attention in most of the countries. The food and agricultural organization recommended that the size of the plot to be proportional to the intensity of agriculture. In irrigated land is small size between 1–5 meters while in rain-fed agriculture size between 10 – 25 square meters and could be extended to 100 square meters (FAO 1981). For Sudan, the plot size has been 100 square meters for some time then became 42 square meters. Now from the experience of agricultural statistics, reach to optimum size of 25 square meters for rain-fed mechanized and 9 square meters for irrigated. Form of the plots: Form of the plot can lead to an error in the estimate due to an error in determining the length of the plot or an error due to plant on the border will be calculated within or outside the plot. To reduce this error the optimum shape of the plot is that who gives us the lower circumference of the specific area. Generally the circular shape is better than square shape and the square shape is better than triangle (India Experience). The square shape has been selected for practical reason. Location of the plot: The location of the plot in the selected farm according to the following: -Reach the selected farm and make sure it is the selected farm. -Collect the primary information about the farm (cultivated area, harvested area, sowing date and the variety sown). 42 -Measure the length and width of each selected farm. -Choose the random length and the random width using the table of random numbers. -start measuring the random length, usually the start from the south-west corner of the farm. -From end point of the random length working towards the width up to the end point of the random width. -The joint point of the random length and the random width is the south-west corner of the first plot -Put the pole in the south-west corner of the plot and then measure the required meters to determine the other pole point using the cross- stuff, then determine the third pole and the fourth pole points by the same way to make square shape as required. -Measure the diagonal to assure that plot measurements are correct. -Do the same to determine the second plot. 17-3Some sampling surveys in Sudan: The National irrigated schemes: The national schemes follow a proper crop rotation, where each crop is planted in a separate piece of land known as number with a definite size of feddanage and usually includes tenancies with equal sizes. Also the lay-out of the canalization system facilitates the estimation of planted areas under each crop. Accordingly, the statistics of area planted are accurate and reliable. The estimation of yield is based on sample survey were crop-cutting is conducted, an example is Gazira scheme, the statistics division of the agricultural planning administration carries an annual survey to estimate yields of the main crops (sorghum, wheat, groundnuts and cotton). As the administration is interested to have information at the level of the block, all blocks are included, as the first stage of selection starts at the tenancy level. In scheme, 36 tenancies were selected from each block resulting 3.2% according for the planted area, in a sample size of 40032 tenancies. The sample design adopted is a multi-stage random sample. In the first stage applying systematic random selection, three canals (Turaa) are selected from each block, representing the start, the middle and the tail of the major canal. In the second stage, from each selected canal three numbers are selected applying simple systematic random selection, also representing the start, the middle and the tail of each number. At the 3rd stage, 3farmers are randomly selected from each selected number, one at the start, one at 43 the middle and one at the tail. At the last stage, 3plots of 2*2 meters are randomly selected at the beginning, the middle and the end of the tenancy. Then the heads are cut dried,threshed and weighted, and the weighted average is calculated to estimate the yield of crop. All the same time paroled estimation which is mainly base on weekly records of the agricultural inspectors is prepared by the agricultural administration. Both estimates are mode available to the top administration. Of the scheme I think so as to avoid duplication and sometimes contradiction, it is better to depend on the objective method adopted by the planning administration and to supply with more facilities and financial capabilities to improve this job.The other national schemes (Rahad, New Halfa, Suki) are using more or less similar procedures of estimation, but Gezira scheme is more experienced in the aspect and its coverage and persistence is better. Other irrigated agricultural schemes: The state ministries of agriculture are responsible for generating the agricultural statistics of the irrigated sector in that state. Although these schemes are having their own agricultural rotation and somewhat similar canalization like the national scheme, but they rarely follow objective method of estimation. The data of area planted and area harvested as fairly good degree of accuracy, and as usually there is a plan for targeted area and a close follow up at area planted and areas to be harvested. An early stage where crops are at maturing stage yields depend on eye estimates, and then refined from acetous records of threshers or combine harvesters at harvest time as crops like sorghum, wheat, broad bean are harvested either fully or partially by combine harvesters or threshers. The accuracy of yield figures in this sub sector can be considered acceptable, as an example we will considered this procedure adopted for collecting agricultural data mainly for food crops in River Nile state. According to the administrative division in the state, they are six localities, at each locality there is an agricultural inspector, assisted by new graduates of agriculture, who are located at administrative unites under the locality. Each locality has an average of about 10basic units. Each assistant inspector is responsible to collect data from their units by interviewing farmers plus his own observations, weekly reports are submitted from each locality from the time land preparation till the time of harvest, giving information about areas, performance of the crop yields and factor affecting the crop type, rain fall, number of irrigation, application of fertilizer, number of weeding, pests, and diseases etc …. At time of harvest, the inspectors try 44 to record the production by following the combine harvester's threshers in the field. The agricultural planning administrationwithin the ministry of agriculture at River Nile state is responsible to prepare a weekly report reflecting the agricultural station at state level. 18-3Rain- fed mechanized sector: Estimation of planted area: The preliminary estimates of area depend to a large exert on the records of the annual renewal of the schemes as the farmers are supposed to pay laud rent before the start of the season. This information is supplemented and refined information of rain fall, prices, and information from farmers. Usually in September team from mechanized farms co-operation (MFC) tour all schemes from door to door to estimate the planted area either by interviewing the farmers or the manager of the scheme or by eye estimation by the members of the team. In November and December, depending on the availability of funds and transportation facilities, the teams estimate the areas to be harvested and the expected yield by subjective methods (eye estimation).The federal administration of agricultural statistics of the ministry of agriculture in calibration with state ministries of agriculture used to carry crop cutting surveys to estimate the yield of sorghum. The intensity of coverage and timeliness of these surveys depend considerably on the availability of financial resources. The coverage of the surveys in season05/2006 was the best during the last 15 years as it covered Gedaref, Damazin, S.Kordofan, Sennar, White Nile and Gedaref being the largest area is chosen as an example to explain the sampling procedure of the crop cutting survey. 19-3Some surveys in Egypt and Inbdia: Study made by AbdElshahid (1973) to estimate the average yield per feddan of cotton in Egypt. The experimental data for this study was obtained from crop cutting surveys made on cotton in the season of 1969 and 1971 to estimate the mean yield of cotton per feddan. The sampling design for these surveys was stratified multi-stage sampling. The study is carried out for different governorates in Egypt through use of crop cutting technique. In each governorate, the number of cluster was calculated for a given number of fields per cluster with different percentage standard errors. Also the optimum numbers of clusters and experimental plots per cluster and with a minimum cost were calculated. The result indicated that sampling two or three 45 fields per cluster with plot per each selected field is about the optimum distribution for estimating the average yield. Ghazi and Sallib conducted a survey on wheat in (1960) in Dakhaliya to compare economical wise between sampling two plots in the same field or samplingtwo fields and sampling one plot in each selected field. The result showed that tge mean square error between fields is highly significant. Thus the variance in yield rate between fields is far greater than that within the same field. They concluded that it is disadvantageous to sample more than one plot per field. Further they concluded that selecting two fields per cluster and conducting one crop cutting experiment in each selected field for crop sampling in Egypt is adequate. Suktame (1947) reported some results of the investigation on different crops. He indicated that there was a definite risk of obtaining over- estimate of the average yield with small plots. The first was in Morad Abad district (1945). He selected eight villages. In each selected village two were marked at random. The field results showed that the average yield for the district decreases and the decreasing rate diminishes with increase in size. This implies that when the plot size is sufficiently large, the estimate attains a stable value. 20-3 Research Type: It is estimation of sorghum yield in rain-fed traditional sector, using crop cutting method by using multi-stage sampling. Design of multi-stage sample: Stratification is the process of dividing members of the population into homogeneous subgroups before sampling. These subpopulations are non-over-lapping, and together they comprise the whole of the population.These are used as primary sampling unit; sometimes a sample is drawn from this primary sampling unit. The sample is then done through other additional stages can be added to constitute what we call the multi-stage sampling. The last sampling unit in the final of sampling is called the listing (ultimate) sampling unit. Where our study is carried out the area is divided into two strata namely the sandy soil strata and clay soil strata. Three administrative units are defined on those strata namely Dalami (clay soil), Fershaya and debaibat (sandy soil). Three villages are selected from these administrative units are taken as first stage sampling, the households as second stage sampling and ultimately the plots as the third stage sampling. 46 Location and marking of crop cutting plot: 1-Make a list of farms in each selected village, and this represents the secondary sampling units (SSU). 2-Random number of farms is selected from each selected (SSU) 3-Two plots are selected from each selected farm (third sampling unit) The location of the plot in the selected farm according to the following: -Reach the selected farm and make sure it is the selected farm. -Collect the primary information about the farm (cultivated area, harvested area, sowing date and the variety sown). -Measure the length and width of each selected farm. -Subtract the plot length and width from the farm length and width to make sure that the plot is inside the farm. -Choose the random length and the random width using the table of random numbers. -start measuring the random length, usually the start from the south-west corner of the farm. -From end point of the random length working towards the width up to the end point of the random width. -The joint point of the random length and the random width is the south-west corner of the first plot -Put the pole in the south-west corner of the plot and then measure the required meters to determine the other pole point using the cross- stuff, then determine the third pole and the fourth pole points by the same way to make square shape as required. -Measure the diagonal to assure that plot measurements are correct. -Cut the crop heads (sorghum) inside the plot and count the heads number and put them in separate sack with a label of farm and plot number and the sector or the locality and heads No: -Do the same to determine the second plot. -This exercise is done to all the samples In the last stage come digging, and threshing weighing to all samples separately and write the weight of each plot on its label, this is done in the field and the data is put in special sheet designed for this purpose, The data entered to the computer for analysis to determine the yield of the crop per unit area to be used in farther analysis 47 Figure (1): Farm map: 1500m Plot 365m one 900m Plot 689m 1094m two 275m Actual length 1500m Random lengths 1500-5 for plot one 365m and1094 m for plot two. Actual width 900m Random widths 900-5 for plot one 689 and 275m for plot two. 21-3Assessment methodology: Two stage estimation: At first stage we select a number of farmers and from each selected farmer two plots are selected randomly. The data is prepared for analysis as follows: Table (1-3) Two stage estimation: No. Plot production Sum of two plots Square of the Sum of two Plot1 Plot2 plots 2 1 Y11 Y12 Y1. Y 1. 2 2 Y21 Y22 Y2. Y 2. 2 3 Y31 Y32 Y3. Y 3. - - - - - 48 ------ 2 n Yn1 Yn2 Yn. Y n. Total 푛 푛 ∑ 푦푖. ∑ 푦푖. = 푘 푖=1 푖=1 Source: Mukhtar (2005) ∑푛 푌푖. ∑푛 푌푖. 1-Plot average production equal to: = 푖=1 = 푖=1 …….. [67-3] 2푛 푛푚 2 [∑푛 푌 ] 2- The correction factor (CF): = 푖=1 푖. …….. [68-3] 2푛 3 – Sum of squares between farmers: = 퐾 − 퐶퐹 = 퐵2 ….. [69-3] 2 푛 2 2 4 – Total sum of squares: = ∑푖=1 ∑푗=1 푦푖푗 − 퐶퐹 = 푇푆푆 ……. [70-3] 5 – Sum of squares within farmers: = TSS - B2 ….. [71-3] Table (2-3) two stage estimation analysis of variance [ANOVA]: Source of variation DF Sum of Squares Mean of Squares E[M.S] 푛 2 2 2 Between farmers n-1 퐵 푆푤 + 2푆푏 2 2 푆2 2 ∑[푦̅푖 − 푦̅..] = 퐵 푛 − 1 1 푖=1 2 Between plots within n TSS - SST 푇푆푆 − 푆푆푇 2 푆푤 = 푆0 farmers 푛 푛 2 2 Total 2n-1 ∑푖=1∑푗=1[푌푖푗 −푌..] Source: Mukhtar (2005) 6 – The variance: 2 2 2 V(푌̅ ) = 푆푏 + 푆푤 = 푆1 ….. [72-3] .. 푛 2푛 2푛 2 2 Where:푆2 = 푆2푆2 = 푆1 − 푆0 ……... [73-3] 푤 0 6 2 7 – The sample Error: 1 S.E (푌̅..) = [푉(푌̅..)]2 ……. [74-3] 8 – The coefficient of variation: 2 2 푆푏 푆푤 ( ̅ ) + C.V. (P) = S.E 푌.. * 100 = √ 푛 2푛 * 100 ……. [75-3] 푌̅.. 푌̅.. ̅ 2 2 2 Or, [ 푃푌 ] = 푆푏 + 푆푤 …….. [76-3] 100 푛 2푛 49 By this we give estimation for yield of the plot along with the variance, In case the 푆2 sample error is small. Otherwise the variance decreased by 1 . 푁 The Estimation of the Overall Yield: The estimation of the overall yield is calculated from the yields of different strata by using the weights of strata as shown in the following table: Table (3-3) The estimation of the overall yield: Stratum 퐴푡 ̅ ̅ 2 2 W = 푌푡 푊푡푌푡 푉(푌̅) 푊 푊 푉(푌̅) 퐴0 푡 푡 푡 푡 1 2 3 - - - 100 푌̅ 0 푉(푌̅0) Source: Mukhtar (2005) Where: At = Area cultivated in stratum t. A0 = Total cultivated area in the whole locality. 1 – Average yield of plot in the locality: ̅ ∑푙 푌0 = 푡=1 푤푡푌̅푡 …….. [77-3] 1 2 - Sample Error: = [푉(푌̅0)]2 ……. [78-3] 1 [푉(푌̅̅̅)]2 3 - Coefficient of variation: = 0 …… [79-3] 푌̅0 4 – 95% confidence limit: = 푌̅0 ± 1.96 ∗ 푆퐸 …… [80-3] Three stages sampling: In this case we select a number of village’s, n and from the selected village we select a number of farmers, m and ultimately we select two plots from the selected farmer, q. The analysis of variance table for three stages sampling as follows: 50 Table (3-4) Three stage estimation analysis of variance (ANOVA): Source of variation DF Sum of Squares Mean of Squares E[M.S.] 푛 2 Between blocks n-1 푆2 2 푚푞 ∑[푦̅̅푖̅.. − 푦̅̅…̅] 푖=1 푛 푚 2 Between tenants within blocks n(m-1) 2 푆1 푞 ∑ ∑[푦̅̅푖푗̅̅. − 푦̅̅푖̅..] 푖=1 푗=1 Between plots within tenants nm(q-1) 푛 푚 푞 푆2 2 0 ∑ ∑ ∑[푦̅̅푖푗푘̅̅̅ − 푦̅̅푖푗̅̅.] 푖=1 푗=1 푘=1 Total nmq-1 푛 푚 푞 2 ∑ ∑ ∑[푦̅̅푖푗푘̅̅̅ − 푦̅̅…̅] 푖=1 푗=1 푘=1 Source: Mukhtar (2005) Where: 푆2 푆2 푆2 푆2 1 - 푉(푌̅̅̅) = 2 + 푏 + 푤 = 푧 …… [81-3] … 푛 푛푚 푛푚푞 푛푚푞 2 2 푆푤 = 푆0 ………… [82-3] 푆2 푆2 푆2 = 1 − 0 …… [83-3] 푏 푞 푆2 푆2 푆2 = 2 − 1 …… [84-3] 푧 푚푞 1 2 - S.E (푌̅...) = [푉(푌̅̅…̅)]2 ….. [85-3] ( ̅ ) 3 – C.V. = S.E 푌… * 100 …… [86-3] 푌̅̅…̅̅ 23-3Multiple comparison of the means procedure: Preface: When the computed value of the F statistic in a single factor ANOVA is not significant, the , analysis is terminated because no differences among the µi s have been identified. But when H0 is , rejected, the investigator will usually want to know which of the µi s are different from one another. A method for carrying out this further analysis is called a multiple comparisons procedure. (Jay L. Devore) 51 Several of the most frequently used procedures are based on the following central idea: First calculate a confidence interval for each pairwise difference, µi - µj with i< j. Thus if I=4, the six required CIs would be for µ1 - µ2 [but not also for µ2 - µ1], µ1 - µ3, µ1 - µ4,µ2 - µ3, µ2 - µ4 and µ3 - µ4. Then if the interval for µ1 - µ2 does not include 0, conclude that µ1 and µ2 differ significantly from one another, if the interval does include 0; the two µ’s are judged not significantly different. Following the same line of reasoning for each of the other intervals, we end up being able to judge for each pair of µ’s whether or not they differ significantly from one another. The procedures based on this idea differ in how the various confidence intervals [CLs] are calculated. Here I present a popular method that controls the simultaneous confidence level for all I (I-1)/2 intervals. Tukey’s procedure: Tukey’sprocedure involves the use of another probability distribution called the student zed range distribution. The distribution depends on two parameters. A numerator dfm and a denominator, dfv. Let Q 훼, m, v denote the upper tail 훼 critical value of the student zed range distribution with m numerator df and v denominator df [analogous to F훼, v1, v2]. Values of Q 훼, m, v are given in the table of critical values for student zed range distributions. (Jay L. Devore) With probability 1- 훼, ̅ ̅ ̅ ̅ 푋푖. − 푋푗. − 푄 푀푆퐸 ≤ µ푖. − µ푗. ≤ 푋푖. − 푋푗. + 푄 푀푆퐸 ………. [87-3] ∝,퐼,퐼(퐽−1)√ ∝,퐼,퐼(퐽−1)√ 퐽 퐽 For every i and j ( i = 1,……..,I and j = 1, ………., I) with i< j. The numerator df for appropriate Q훼 critical value is the number of population or means being compared, and not I-1 as in the F test. When the computed 푿̅풊., 푿̅풋. and MSE are substituted into the upper proportion, the result is a collection of confidence intervals with simultaneous confidence level 100(1 – 훼) % for all pairwise differences of the form µi. − µj. with i 52 Since we are not really interested in the lower and upper limits of the various intervals but only in which include 0 and which do not, much of the arithmetic associated with the above proposition can be avoided. The differences can be identified visually using an “underscoring pattern” as shown in the following the T method for identifying significantly different µj , 푠 ∶ Select 훼, extract푄∝,퐼,퐼(퐽−1) from the table and calculate w = 푄 푀푆퐸. Then list the ∝,퐼,퐼(퐽−1)√ 퐽 sample means in increasing order and underline those pairs that differ by less than w. Any pair of sample means not under scored by the same line corresponds to a pair of population or treatment means that are judged significantly different. Fortunately these very complicated calculations are simply reached using statisticalsoftware’s developed for these purposes. Here I used SPSS packages’ in analysis of my experiments. 53 CHAPTER FOUR 1-4 The Analysis and Results Discussion 54 Chapter Four Analysis and Results Discussion 1-4 The analysis and results discussion:- Number of heads per feddan:- An experiment was carried out in three different areas to compare three different plot sizes and their impact on estimation of the number of heads per feddan. Let µi denotes the average number of heads given by plot i, filters (i = 1… 3). A sample of 22 farmers for each plot size was used, resulting in the following sample means: Fershaya Area (First stratum – loam soil): A sample of twenty two farmers for each plot size was used, resulting in the following sample means:Plot size 5x5 = 4418, plot size 6x7 = 9302 and plot size 10x10 = 6585, while the highest standard deviation shown by using plot size 6x7 meters (4543.546) followed by plot size 5x5 meters (3127.879) and plot 10x10 meters (2107.397) and the highest standard error shown by using also plot size 6x7 meters (1015.968) followed by using 5x5 meters (699.415)and plot size 10x10meters (471.228), for the coefficient of variation the highest is shown by using plot size 5x5meters (15.8296) followed by plot size 6x7 meters (10.92145) and plot size 10x10 meters (7.155433) as shown in the table (1-4) below. Table (1-4): Mean statistics for number of heads per feddan under different plot sizes: Std. Plot Mean Error CV Std. Deviation plot size 5x5 meters 4418.40 3127.879 699.415 15.8296 `plot size 6x7 meters 9302.50 4543.546 1015.968 10.92145 plot size 10x10 meters 6585.60 2107.397 471.228 7.155433 Total 6768.83 3910.122 504.795 7.45763 Source: Researcher data Table (2-4): Analysis of variance table (ANOVA): Source of Variation Sum of Squares df Mean Square F Sig. Between Groups 2.396E+08 2 1.198E+08 10.305 .000 Within Groups 6.625E+08 57 1.162E+07 Total 9.021E+08 59 Source: Researcher data Since F = 10.305 and p-value = 0.000 as shown in table (2-4) above, H0 is rejected decisively at level 0.05. Because the computed value of the F statistic in a single factor ANOVA is significant. We conclude that 55 there are significant differences between means as judged by the mean under the control condition. We , , now use Tukey s procedure to look for significant differences among the µi s as shown in table (4-3) below. Table (3-4): Sub-set homogeneous: CV Subset for alpha = 0.05 Plot size N 1 2 plot size 5x5 meters 20 4418.40 15.8296 plot size 10x10 meters 20 6585.60 7.155433 plot size 6x7 meters 20 9302.50 10.92145 Sig. .119 1.000 Source: Researcher data , Refer to the analysis output the above table (3-4) represent the differences among the µi s. The plot size 6x7 meters is significantly different from the other two namely plot size 5x5 meters and the plot size 10x10 meters in its true average content. On the other hand the plot size 5x5 meters and the plot size 10x10 meters are not significantly different from one another in their true average contents. Debaibat (Second stratum – Sandy soil): In Debaibat area a sample of twenty two farmers for each plot size was used, resulting in the following: sample means:Plot size 5x5 = 7404, plot size 6x7 = 4417 and plot size 10x10 = 9201heads per feddan while the highest standard deviation shown by using plot size 10x10 meters (4632.815) followed by plot size 5x5 meters (3128.110) and plot 5x5 meters (2187.275) and the highest standard error shown by using also plot size 10x10 meters (1035.929) followed by using 6x7 meters (699.467)and plot size 5x5meters (489.090), for the coefficient of variation the highest is shown by using plot size 6x7meters (15.83399) followed by plot size 10x10 meters (11.25869) and plot size 5x5 meters (6.605213)as shown in the table (4-4) below. Table (4-4): Mean statistics for number of heads per feddan under different plot sizes: Plot size Mean Std. Deviation Std. Error CV plot size 5x5 meters 7404.60 2187.275 489.090 6.605213 plot size 6x7 meters 4417.50 3128.110 699.467 15.83399 plot size 10x10 meters 9201.15 4632.815 1035.929 11.25869 Total 7007.75 3944.896 509.284 7.267437 Source: Researcher data 56 Table (5-4): Analysis of variance table (ANOVA): Source of Variation Sum of Squares df Mean Square F Sig. Between Groups 2.336E+08 2 1.168E+08 9.723 .000 Within Groups 6.846E+08 57 1.201E+07 Total 9.182E+08 59 Source: Researcher data In the analysis of variance table (5-4) above F = 9.723 and p-value = 0.000, H0 is rejected decisively at level 0.05. Because the computed value of the F statistic in a single factor ANOVA is significant. We conclude that there are significant differences between means as judged by the mean under the control , , condition. We now use Tukey s procedure to look for significant differences among the µi s as shown in table (4-6) below. Table (6-4): Sub-set homogeneous: Plot size N Subset for alpha = 0.05 CV 1 2 plot size 6x7 meters 20 4417.50 15.83399 plot size 5x5 meters 20 7404.60 6.605213 plot size 10x10 20 9201.15 11.25869 meters Sig. 1.000 .238 Source: Researcher data , The analysis output in the above table (6-4) represent the differences among the µi s. The plot size 5x5 metersand plot size10x10 are not significantly different from one anotherin their true average contents. On the other hand the plot size 5x5 meters and the plot size 10x10 meters are significantly different from plot size6x7meters. Dalami: (Third stratum – Clay soil) In Dalami area a sample of twenty two farmers for each plot size was used, resulting in the following: sample means: Plot size 5x5 = 9739, plot size 6x7 = 7027 and plot size 10x10 = 3931heads per feddan, while the highest standard deviation shown by using plot size 5x5 meters (5003.058) followed by plot size 6x7 meters (2623.802) and plot 10x10 meters (2451.364) and the highest standard error shown by using also plot size 5x5 meters (1118.718) followed by using 6x7 meters (586.700)and plot size 10x10meters (548.142), for the coefficient of variation the highest is shown by using plot size 10x10 meters (13.94337) followed by plot size 5x5 meters (11.48604) and plot size 6x7 meters (8.348629) as shown in the table (7-4). 57 Table (7-4): Mean statistics for number of heads per feddan under different plot sizes: Plot Mean Std. Deviation Std. Error CV plot size 5x5 meters 9739.80 5003.058 1118.718 11.48604 plot size 6x7 meters 7027.50 2623.802 586.700 8.348629 plot size 10x10 meters 3931.20 2451.364 548.142 13.94337 Total 6899.50 4235.539 546.806 7.925296 Source: Researcher data Table (4-8): Analysis of variance table (ANOVA): Source of Variation Sum of Squares df Mean Square F Sig. Between Groups 3.379E+08 2 1.689E+08 13.364 .000 Within Groups 7.206E+08 57 1.264E+07 Total 1.058E+09 59 Source: Researcher data In the analysis of variance table (4-8) above F = 13.364 and p-value = 0.000, H0 is rejected decisively at level 0.05. Because the computed value of the F statistic in a single factor ANOVA is significant. We conclude that there are significant differences between means as judged by the mean under the control , , condition. We now use Tukey s procedure to look for significant differences among the µi s as shown in table (4-9) below. Table (4-9): Sub-set homogeneous: Plot size N Subset for alpha = 0.05 CV 1 2 3 plot size 10x10 meters 20 3931.20 13.94337 plot size 6x7 meters 20 7027.50 8.348629 plot size 5x5 meters 20 9739.80 11.48604 Sig. 1.000 1.000 1.000 Source: Researcher data , The analysis output in the above table (4-9) represent the differences among the µi s. The plot size 5x5 meters, plot size6x7 and plot size 10x10 are significantly different from one another in their true average contents. On the other hand the plot size 5x5 metersis higher followed by plot size 6x7meters. 4-1-2 The average yield per feddan: 4-1-2-1 Fershaya(First stratum – loam soil): In the other experiment which was carried outto compare the effectof different plot sizeson average yield per feddan as judged by the controlled conditionLet µi denotes the average yield given by plot ifilters (i = 1… 3). A sample of 22 farmers for each plot size was 58 used, resulting in the following sample means:Plot size 5x5 = 75.18, plot size 6x7 = 97.25 and plot size 10x10 = 94.07, while the highest standard deviation shown by using plot size 6x7 meters (72.364) followed by plot size 10x10 meters (71.783) and plot 5x5 meters (67.905) and the highest standard error shown by using also plot size 6x7 meters (16.181) followed by using 10x10 meters (16.051)and plot size 5x5meters (15.184), for the coefficient of variation the highest is shown by using plot size 5x5 meters (20.19694) followed by plot size 10x10 meters (17.06262) and plot size 6x7 meters (16.63914) as shown in the table (10-4) below. Table (10-4): Mean statistics for average yield per feddan under different plot sizes: Plot Mean Std. Deviation Std. Error CV plot size 5x5 meters 75.18 67.905 15.184 20.19694 plot size 6x7 meters 97.25 72.364 16.181 16.63914 plot size 10x10 94.07 71.783 16.051 meters 17.06262 Total 88.83 70.194 9.062 10.20111 Source: Researcher data Table (11-4): Analysis of variance table (ANOVA): Source of Variation Sum of Squares df Mean Square F Sig. Between Groups 5693.243 2 2846.622 .569 .569 Within Groups 285010.700 57 5000.188 Total 290703.943 59 Source: Researcher data Since F = .569 and P-value = 0.569, H0 is not rejected decisively at level 0.05. We conclude that there are no significant differences between means as judged by the mean under the control condition as shown in table(11-4) above. Because the computed value of the F statistic in a single factor ANOVA is not , significant, the analysis is terminated because no differences among the µi s have been identified as shown in table (4-12)below. Table (12-4): Sub-set homogeneous: CV Subset for alpha = 0.05 Plot size N 1 plot size 5x5 meters 20 75.18 20.19694 plot size 10x10 meters 20 94.07 17.06262 plot size 6x7 meters 20 97.25 16.63914 Sig. .588 Source: Researcher data 59 Refer to the analysis output in table (10-4) above represents the differentCV,s, you can see thatplot size 6x7 has the lower CV (16.63914), followed by plot size 10x10 (17.06262) and plot size 5x5 (20.19694).We conclude that plot size 6x7 is better in estimation than the two other plots. Debaibat (Second stratum – Sandy soil): In Debaibat area the experiment which was carried outto compare the effectofdifferent plot sizeson average yield per feddan as judged by the controlled conditionLet µi denotes the average yield given by plot ifilters (i = 1… 3). A sample of 22 farmers for each plot size was used, resulting in the following sample means: Plot size 5x5 = 103.49, plot size 6x7 = 75.18 and plot size 10x10 = 97.25, while the highest standard deviation shown by using plot size 10x10 meters (72.364) followed by plot size 5x5 meters (67.961) and plot 6x7 meters (67.906) and the highest standard error shown by using also plot size 10x10 meters (16.181) followed by using 5x5 meters (15.196)and plot size 6x7meters (15.184), for the coefficient of variation the highest is shown by using plot size 6x7 meters (20.19704) followed by plot size 10x10 meters (16.63861) and plot size 5x5 meters (14.68426), as shown in the table (13-4) below. Table (13-4): Mean statistics for number of heads per feddan under different plot sizes: Plot size Mean Std. Deviation Std. Error CV plot size 5x5 meters 103.49 67.961 15.196 14.68426 plot size 6x7 meters 75.18 67.906 15.184 20.19704 plot size 10x10 meters 97.25 72.364 16.181 16.63861 Total 91.97 69.344 8.952 9.733662 Source: Researcher data Table (4-14): Analysis of variance table (ANOVA): Source of Variation Sum of Squares df Mean Square F Sig. Between Groups 8848.925 2 4424.463 .918 .405 Within Groups 274860.108 57 4822.107 Total 283709.034 59 Source: Researcher data Since F = .918 and P-value = 0.405, H0 is not rejected decisively at level 0.05. We conclude that there are no significant differences between means as judged by the mean under the control condition as shown in table (4-14). Because the computed value of the F statistic in a single factor ANOVA is not , significant,the analysis is terminated because no differences among the µi s have been identified as shown in table (4-15)below. 60 Table (4-15): Sub-set homogeneous: Plot size N Subset for alpha = 0.05 CV 1 plot size 6x7 meters 20 75.18 20.19704 plot size 10x10 meters 20 97.25 16.63861 plot size 5x5 meters 20 103.49 14.68426 Sig. .407 Source: Researcher data Refer to the analysis output in table (4-13) aboverepresents the differentCV,s, you can see thatplot size 5x5 has the lower CV (14.68426), followed by plot size 10x10 (16.63861) and plot size 6x7 (20.19704).We conclude that plot size 5x5 is better in estimation than the two other plots. Dalami (Third stratum – Clay soil): In the other experiment which was carried out in Delami areato compare the effectof different plot sizeson average yield per feddan as judged by the controlled condition.Let µi denotes the average yield given by plot ifilters (i = 1… 3). A sample of 22 farmers for each plot size was used, resulting in the following sample means: Plot size 5x5 = 104.12, plot size 6x7 = 97.22 and plot size 10x10 = 65, while the highest standard deviation shown by using plot size 5x5 meters (70.662) followed by plot size 6x7 meters (70.028) and plot 10x10 meters (44.881) and the highest standard error shown by using also plot size 5x5 meters (15.801) followed by using 6x7 meters (15.659)and plot size 10x10meters (10.036), for the coefficient of variation the highest is shown by using plot size 6x7 meters (16.10616) followed by plot size 10x10 meters (15.44056) and plot size 5x5 meters (15.17502) as shown in the table (16-4) below. Table (16-4): Mean statistics for number of heads per feddan under different plot sizes: Plot size Mean Std. Deviation Std. Error CV plot size 5x5 meters 104.12 70.662 15.801 15.17502 plot size 6x7 meters 97.22 70.028 15.659 16.10616 plot size 10x10 meters 65.00 44.881 10.036 15.44056 Total 88.78 64.277 8.298 9.34692 Table (17-4): Analysis of variance table (ANOVA): Source of Variation Sum of Squares df Mean Square F Sig. Between Groups 17447.703 2 8723.851 2.197 .120 Within Groups 226316.306 57 3970.462 Total 243764.009 59 Source: Researcher data 61 Since F = 2.197 and P-value = 0.120, H0 is not rejected decisively at level 0.05. We conclude that there are no significant differences between means as judged by the mean under the control condition as shown in table (4-17) above. Because the computed value of the F statistic in a single factor ANOVA is , not significant, the analysis is terminated because no differences among the µi s have been identified as shown in table (4-18)below. Table (18-47): Sub-set homogeneous: Plot size N Subset for alpha = 0.05 CV 1 plot size 10x10 meters 20 65.00 15.44056 plot size 6x7 meters 20 97.22 16.10616 plot size 5x5 meters 20 104.12 15.17502 Sig. .131 Source: Researcher data Refer to the analysis output in table (4-16) above represents the differentCV,s, you can see thatplot size 5x5 has the lower CV (15.17502), followed by plot size 10x10 (15.44056) and plot size 6x7 (16.10616).We conclude that plot size 5x5 is better in estimation than the two other plots. 62 CHAPTER FIVE 1-5 Conclusion 2-5 Recommendation 63 Chapter Five Conclusion and recommendations of the Research Conclusion: This study revealed that the: 1- The higher plant density obtained with medium plots size in stratum one(loam soils) with no significant difference between large and small size plots, while in stratum two (sandy soils) the higher estimation obtainedwith large plots size, but with no significant difference from medium size plots. In the third stratum (clay soils) the higher plant density estimation obtained with small size plots with no significant difference from medium size plots. 2- The standard deviation is lower for large size plots in the loam and clay soils while in sandy soils is lower for small size plots. 3- In the loam soils the large size plots had lower coefficient of variation while in the sandy soils the small size plots shows lower coefficient of variation and the medium size plots has the lower coefficient of variation in the clay soils. 4- The higher crop yield obtained with medium plots size in stratum one (loam soils) with no significant difference between all plots, while in stratum two (sandy soils) the higher Estimation of yield obtained with small plots size, but also with no significant difference. In the third stratum (clay soils) as in the second stratum the higher crop yield estimation obtained with small size plots with no significant difference between all plots. 5- The standard deviation is lower for large size plots in the loam and clay soils while in sandy soils is lower for small size plots. 6- In the clay soils the large size plots had lower coefficient of variation while in the sandy soils the medium size plots shows lower coefficient of variation but almost similar to that of small size plots and the small size plots has the lower coefficient of variation in the loam soils. 7- In case of plant density estimation the large size plots are better to use in clay and sandy soils while small is better in the sandy soils. 8- Since there is no significant difference between large and small plots in the first stratum and also no significant difference between large and medium plots in the second stratum, beside there is no significant difference small and medium size plots, we conclude that 64 large size plots were better in the loam and sandy soils while medium size plots are better in the clay soils. 9- Since there was no significant difference between all plots sizes in estimation of yield in different soils types we conclude that any plot size may be use in estimation. Therefore according to the conclusions of the study the plot size had not shown any effect on the yield in different types of soils, but there was slight effect of plots size in case of plants density estimation. There seem other factors affecting the level of yields. These factors should be planting spaces, seed rate, adequate re-sowing, thinning and optimum sowing dates. Recommendation: 1- If the main objective of the survey is to estimate the crop yield, then the small size plots are better and recommended to use in all types of soils to save time and to save resources. 2- If the objective of the survey is to estimate the plant density then the medium plots size are better in estimation and recommended to be used. 3- Utilize methods and means of collecting, processing, analyzing, and presenting data that meet reasonable standards of accuracy, coverage and timeliness, while at the same time try to minimize financial and human costs. 4- Have institutional structure which brings users and suppliers of information in a continuous dialogue and which is able to adapt itself to the changing demands of information and modern methodologies for generating it. 5- General perception and understanding of the importance of information system by decision makers, politicians, planners and most categories of data users must followed of adoption and application reality to raise the standard of agricultural statistics. 6- Agricultural census must be conducted to provide skeleton data for efficient statistical list frames. 7- Crop cutting surveys must be adopted to cover all the other crops and in all agricultural sectors. 8- Crop cutting surveys must be used to estimate field base pre-harvest and harvest loss of crops. 9- Utilize modern technology to provide area sampling frame to substitute list frame. 65 References 1- Elements of Survey Sampling Notes prepared for Swedish Agency for Research By: Tore Dalenius 2- Leslie Kish Selected Papers Edited by:Graham Kalton and Steven Heeringa 3- Principles and Procedures of Statistics, A Biometrical Approach Second Edition Robert G. D. Steel Professor of Statistics North Carolina University James H. Torrie Late Emeritus Professor of Agronomy, University of Wisconsin 4- Sampling Techniques Third Edition William G. Cochran Professor of Statistics, Emeritus Harvard University 5- Probability and Statistics for Engineering and the Sciences Eighth Edition Jay L, Devore 6- Statistical Annual Reports, Department of Agricultural Statistics, Khartoum 7- Strategy for Development of Traditional Rain-fed Agriculture Mamoun Behairy Centre for Economic and Social Studies and Research in Africa(October 2013) المراجع العربية: 1- المسوحات الزراعية بالسودان – التامل واالستشراق الخرطوم 2005 مختار ابراهيم احمد 2- تقارير مسوحات قطع المحصول السنوية ادارة االحصاء الزراعي وزارة الزراعة االتحادية الخرطوم 66 Annexes 67 Annex (1) Plot size, number of heads and weight per plot of the first stratum: Farm Plot size 5x5 Plot size 6x7 Plot size 10x10 No. PLt1h PLt2h PLt1w PLt2w PLt1h PLt2h PLt1w PLt2w PLt1h PLt2h PLt1w PLt2w 1 0 35 0 750 121 79 957 630 248 172 3200 2000 2 22 35 220 650 60 153 1260 1428 220 236 6200 6800 3 4 8 350 640 110 24 284 294 0 68 0 800 4 22 12 150 180 32 136 2100 2016 188 164 3800 3800 5 18 11 250 225 40 54 2076 1764 164 184 6800 5200 6 15 9 350 270 73 181 3360 2554 156 188 2200 1800 7 14 18 90 40 69 64 1596 1722 128 148 3600 4000 8 41 35 200 300 52 230 865 840 188 0 1800 0 9 9 22 70 170 128 114 1260 571 192 104 2600 2080 10 19 0 200 0 60 69 991 1428 124 100 2680 1600 11 22 0 750 0 146 150 1764 344 144 140 1000 1520 12 42 25 25 500 55 30 235 84 100 92 3000 1200 13 29 21 700 300 99 0 823 0 128 204 2800 540 14 12 8 200 190 0 5 0 17 352 72 4400 720 15 14 9 400 180 94 42 1092 252 192 256 219 680 16 38 33 1350 1100 138 82 252 521 40 344 114 660 17 62 63 1550 1600 55 123 269 680 112 316 400 3600 18 58 69 1550 750 77 168 991 722 24 248 720 840 19 32 39 250 300 193 220 882 706 44 216 220 1000 20 37 90 400 700 81 114 496 773 116 160 2600 2400 source: Field survey 2015/2016 68 Annex (2) Plot size, number of heads and weight per plot of the second stratum: Farm Plot size 5x5 Plot size 6x7 Plot size 10x10 No. PLt1h PLt2h PLt1w PLt2w PLt1h PLt2h PLt1w PLt2w PLt1h PLt2h PLt1w PLt2w 1 62 43 800 500 0 59 0 1260 288 188 2279 1500 2 55 59 1550 1700 37 59 370 1092 144 364 3000 3400 3 78 17 650 200 7 13 588 1075 162 56 676 700 4 47 41 950 950 37 20 252 302 76 324 5000 4800 5 41 46 1700 1300 30 18 420 378 95 128 4944 4200 6 39 47 550 450 25 15 588 454 174 432 8000 6080 7 32 37 900 1000 24 30 151 67 164 152 3800 4100 8 47 22 450 1200 69 59 336 504 124 548 2060 2000 9 48 26 650 520 15 37 118 286 304 272 3000 1360 10 31 25 670 400 32 0 336 0 144 164 2360 3400 11 36 35 250 380 37 0 1260 0 348 356 4200 820 12 25 23 750 300 71 42 42 840 132 72 560 200 13 32 51 700 135 49 35 1176 504 236 0 1960 0 14 88 18 1100 180 20 13 336 319 0 12 0 40 15 18 64 115 170 24 15 672 302 224 100 2600 600 16 31 86 110 165 64 55 2268 1848 328 196 600 1240 17 78 79 350 900 104 106 2604 2688 132 292 640 1620 18 60 62 180 210 97 116 2604 1260 184 400 2360 1720 19 11 54 55 250 54 66 420 504 460 524 2100 1680 20 29 40 650 600 62 151 672 1176 192 272 1180 1840 source: Field survey2015/2016 69 Annex (3) Plot size, number of heads and weight per plot of the third stratum: Farm Plot size 5x5 Plot size 6x7 Plot size 10x10 No. PLt1h PLt2h PLt1w PLt2w PLt1h PLt2h PLt1w PLt2w PLt1h PLt2h PLt1w PLt2w 1 72 47 700 750 104 72 1344 840 0 140 0 3000 2 36 91 750 850 92 99 2604 2856 88 140 880 2600 3 31 14 1300 175 0 29 0 336 16 32 1400 2560 4 91 81 1250 1200 79 69 1596 1596 88 48 600 720 5 43 32 1236 1050 69 77 2856 2184 72 44 1000 900 6 103 108 2000 1520 66 79 924 756 60 36 1400 1080 7 41 38 950 1025 54 62 1512 1680 56 72 360 160 8 18 137 515 500 79 0 756 0 164 140 800 1200 9 76 68 750 340 81 44 1092 874 36 88 280 680 10 36 41 590 850 52 42 1126 672 76 0 800 0 11 87 89 1050 205 60 59 420 638 88 0 3000 0 12 33 18 140 50 42 39 1260 504 168 100 100 2000 13 59 0 490 0 54 86 1176 227 116 84 2800 1200 14 0 3 0 10 148 30 1848 302 48 32 800 760 15 56 25 650 150 81 108 932 286 56 36 1600 720 16 82 49 150 310 17 144 48 277 52 132 2700 4400 17 33 73 160 405 131 133 588 1512 84 252 2200 6400 18 46 100 590 430 101 104 302 353 32 276 3200 3000 19 115 131 525 420 18 91 92 420 128 156 1000 1200 20 48 68 295 460 49 67 1092 1008 148 360 1600 2800 source: Field survey 2015/2016 70 Annex 4:TABLE I ONE DIGIT RANDOM NUMBERS ROW COLUM NO. NO 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 9 7 9 3 7 8 0 4 8 9 3 8 5 2 1 5 4 7 3 4 7 6 3 4 7 6 6 4 3 7 9 8 1 5 5 1 7 4 5 1 2 7 2 4 1 9 4 7 3 1 7 6 3 9 7 9 4 6 5 4 0 5 2 8 7 6 3 0 5 2 0 1 3 6 7 5 4 7 2 9 4 8 2 6 7 4 8 5 7 2 4 4 5 4 9 6 8 1 3 5 7 9 6 8 8 0 2 2 5 0 7 2 7 4 2 1 9 9 9 8 9 9 2 8 6 7 9 9 0 9 1 8 6 10 2 5 2 3 4 2 6 8 9 9 2 7 1 7 11 4 9 6 4 3 1 8 6 1 0 6 6 8 3 12 9 0 2 8 2 3 4 1 0 8 2 5 5 1 13 2 1 3 6 8 2 7 4 5 0 8 8 3 0 14 6 0 4 3 7 3 1 6 9 9 4 5 5 9 15 8 3 6 1 1 0 8 1 9 6 0 7 3 3 16 6 2 1 6 2 5 8 9 7 6 1 3 9 1 17 7 2 8 0 8 5 7 1 3 1 2 8 0 5 18 7 2 6 7 5 2 5 3 3 3 6 4 8 5 19 7 7 5 2 6 2 4 7 5 8 5 6 3 2 20 5 4 5 0 3 8 7 1 1 1 5 3 8 2 21 3 2 3 7 0 5 7 1 9 6 3 3 4 0 22 1 8 8 3 2 3 8 2 2 0 0 3 8 8 23 2 9 4 9 6 8 5 8 0 7 4 6 1 2 24 2 4 3 2 4 9 0 9 4 5 3 9 3 4 25 3 5 9 9 6 0 6 2 5 5 2 2 6 7 Annex 5:TABLE 11 –TWO DIGIT RANDOM NUMBERS ROW COLUM NO. NO 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 57 60 10 15 10 49 75 78 18 90 03 40 29 32 2 35 34 56 09 88 41 86 70 53 37 28 23 31 99 3 27 72 79 98 56 31 90 21 44 36 14 72 56 19 4 33 52 77 60 53 60 68 94 09 63 11 51 41 63 5 72 82 21 16 27 70 24 47 42 32 30 39 85 95 6 24 21 30 03 59 42 64 16 72 08 79 35 47 73 7 53 15 27 03 33 38 16 12 00 58 20 76 04 76 8 64 65 12 18 35 06 35 38 06 37 69 22 66 63 9 94 20 09 87 72 45 51 64 79 40 22 42 08 89 10 09 33 49 00 67 18 46 43 79 13 40 92 72 44 11 41 29 22 42 47 64 61 59 68 68 98 96 72 44 12 10 94 23 31 77 84 87 98 47 97 95 11 57 99 13 76 71 62 57 34 73 39 98 22 87 17 83 59 50 14 47 11 36 90 55 31 12 77 00 64 82 44 13 48 15 91 15 93 12 45 65 85 87 35 81 06 80 82 67 16 44 91 89 02 70 52 94 68 55 07 53 34 43 26 17 04 29 41 07 08 53 57 07 31 83 31 68 80 43 18 95 12 26 23 18 37 29 91 51 02 51 35 46 18 19 49 03 29 47 27 97 16 51 51 17 10 48 15 46 20 66 61 70 37 38 15 92 67 00 79 96 77 33 40 21 39 96 83 17 90 12 09 62 63 18 46 33 26 66 22 50 48 63 31 16 96 84 44 22 05 92 42 61 44 23 04 95 51 54 95 88 38 40 55 12 06 40 70 52 24 50 03 99 08 86 17 76 98 40 59 88 90 04 91 25 81 07 74 01 70 31 22 05 76 52 07 60 77 36 71 Annex 6:TABLE111 – A OF THREE DIGIT RANDOM NUMBERS ROW COLUM NO NO . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 102 947 440 753 752 759 802 448 988 211 962 801 396 161 2 753 662 739 760 120 872 972 973 373 906 665 921 386 954 3 962 118 554 665 277 105 078 550 150 068 002 239 308 626 4 371 934 342 484 778 020 472 034 410 129 684 653 582 970 5 505 214 344 083 916 324 353 299 694 364 552 663 558 573 6 436 257 339 275 916 174 903 864 768 284 386 707 947 515 7 235 025 286 775 843 797 441 760 183 624 763 745 220 333 8 431 919 115 608 187 815 924 921 171 791 475 855 562 187 9 048 189 181 257 368 651 571 077 633 676 475 061 011 287 10 298 784 354 029 676 923 092 885 025 146 832 741 726 374 11 041 803 168 009 961 486 370 953 745 025 478 339 571 860 12 412 003 620 779 342 018 700 115 866 510 432 252 080 822 13 150 309 286 080 588 255 712 266 773 128 092 230 000 981 14 926 805 890 637 989 513 389 256 430 501 631 533 579 301 15 782 246 748 302 960 312 279 907 734 643 347 602 513 065 16 547 770 055 859 506 916 431 044 184 362 484 064 919 144 17 472 078 091 855 595 362 485 866 426 897 565 934 748 838 18 841 497 453 355 794 063 114 674 897 855 582 887 726 759 19 506 508 905 685 294 441 723 106 329 899 651 361 648 329 20 188 746 117 340 936 942 876 616 770 672 769 737 097 068 21 648 618 520 017 240 178 862 570 961 252 659 198 117 773 22 527 177 163 439 899 550 154 221 648 762 000 150 284 747 23 201 232 015 597 643 972 353 256 400 324 286 429 975 845 24 883 382 991 330 564 764 143 888 694 703 574 189 172 560 25 363 821 762 199 771 516 659 759 477 645 571 045 699 084 72 Annex 7: The questionnaire: Sudan University of Science and Technology College of Post- Graduate Studies Questionnaire for Estimation of Sorghum Yield (Crop-cutting) General Information: State Locality Admin Unit Farmer Name : Cultivated Area ( ) Fedd. Harvested Area ( ) Fedd. Field Diagram: The Length ( ) Meter The Width ( ) Meter 2 – Crop-cutting Results: Plot Number (1): Plot No. (1) Page No. Column No. Row The Random Number No. Plot Selection: The Length (Field Length – Plot Length) The Width (Field Width – Plot Width) A = ------Meter B = ------Meter C = ------Meter Plot (1) Crop cutting results: Number of Heads The weight (gram) Empty sack weight The net weight 73 Plot Number (2): Plot No. (2) Page No. Column No. Row The Random Number No. Plot Selection: The Length (Field Length – Plot Length) The Width (Field Width – Plot Width) A = ------Meter B = ------Meter C = ------Meter Plot (2) Crop cutting results: Number of Heads The weight (gram) Empty sack weight The net weight 74